Search results for: complement of probability

Authors: Kennedy Efosa Ehimwenma, Sujatha Krishnamoorthy, Safiya Al‑Sharji

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The probability computation of events is in the interval of [0, 1], which are values that are determined by the number of outcomes of events in a sample space S. The probability Pr(A) that an event A will never occur is 0. The probability Pr(B) that event B will certainly occur is 1. This makes both events A and B a certainty. Furthermore, the sum of probabilities Pr(E₁) + Pr(E₂) + … + Pr(Eₙ) of a finite set of events in a given sample space S equals 1. Conversely, the difference of the sum of two probabilities that will certainly occur is 0. This paper first discusses Bayes, the complement of probability, and the difference of probability for occurrences of learning-events before applying them in the prediction of learning objects in student learning. Given the sum of 1; to make a recommendation for student learning, this paper proposes that the difference of argMaxPr(S) and the probability of student-performance quantifies the weight of learning objects for students. Using a dataset of skill-set, the computational procedure demonstrates i) the probability of skill-set events that have occurred that would lead to higher-level learning; ii) the probability of the events that have not occurred that requires subject-matter relearning; iii) accuracy of the decision tree in the prediction of student performance into class labels and iv) information entropy about skill-set data and its implication on student cognitive performance and recommendation of learning.

Keywords: complement of probability, Bayes’ rule, prediction, pre-assessments, computational education, information theory

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Authors: Juliet Udoudom

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Complement ordering principles of natural language phrases (XPs) stipulate that Head terms be consistently placed phrase initially or phrase-finally, yielding two basic theoretical orders – Head – Complement order or Complement – Head order. This paper examines the principles which determine complement ordering in English V- and N-bar structures. The aim is to determine the extent to which complement linearisations in the two phrase types are consistent with the two theoretical orders outlined above given the flexible and varied nature of natural language structures. The objective is to see whether there are variation(s) in the complement linearisations of the XPs studied and the implications which such variations hold for the inter-language syntax of English and Ibibio. A corpus-based approach was employed in obtaining the English data. V- and -N – bar structures containing complement structures were isolated for analysis. Data were examined from the perspective of the X-bar and Government – theories of Chomsky’s (1981) Government-Binding format. Findings from the analysis show that in V – bar structures in English, heads are consistently placed phrase – initially yielding a Head – Complement order; however, complement linearisation in the N – bar structures studied exhibited parametric variations. Thus, in some N – bar structures in English the nominal head is ordered to the left whereas in others, the head term occurs to the right. It may therefore be concluded that the principles which determine complement ordering are both Language – Particular and Phrase – specific following insights provided within Phrasal Syntax.

Keywords: complement order, complement–head order, head–complement order, language–particular principles

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Authors: Juliet Udoudom

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Inappropriate complement selection constitutes one of the major features of non-standard complementation in the Nigerian users of English output of sentence construction. This paper investigates complement clause choice in Written Educated Nigerian English (ENE) and offers some results. It aims at determining preferred and dispreferred patterns of complement clause selection in respect of verb heads in English by selected Nigerian users of English. The complementation data analyzed in this investigation were obtained from experimental tasks designed to elicit complement categories of Verb – Noun -, Adjective – and Prepositional – heads in English. Insights from the Government – Binding relations were employed in analyzing data, which comprised responses obtained from one hundred subjects to a picture elicitation exercise, a grammaticality judgement test, and a free composition task. The findings indicate a general tendency for clausal complements (CPs) introduced by the complementizer that to be preferred by the subjects studied. Of the 235 tokens of clausal complements which occurred in our corpus, 128 of them representing 54.46% were CPs headed by that, while whether – and if-clauses recorded 31.07% and 8.94%, respectively. The complement clause-type which recorded the lowest incidence of choice was the CP headed by the Complementiser, for with a 5.53% incident of occurrence. Further findings from the study indicate that semantic features of relevant embedding verb heads were not taken into consideration in the choice of complementisers which introduce the respective complement clauses, hence the that-clause was chosen to complement verbs like prefer. In addition, the dispreferred choice of the for-clause is explicable in terms of the fact that the respondents studied regard ‘for’ as a preposition, and not a complementiser.

Keywords: complement, complement clause complement selection, complementisers, government-binding

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Authors: Ahmet Kaya

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Incoming cash flows and outgoing claims play an important role to determine how is companies’ profit or loss. In this matter, ruin probability provides to describe vulnerability of the companies against ruin. Quantum mechanism is one of the significant approaches to model ruin probability as stochastically. Using the Hamiltonian method, we have performed formalisation of quantum mechanics < x|e-ᵗᴴ|x' > and obtained the transition probability of 2x2 and 3x3 matrix as traditional and eigenvector basis where A is a ruin operator and H|x' > is a Schroedinger equation. This operator A and Schroedinger equation are defined by a Hamiltonian matrix H. As a result, probability of not to be in ruin can be simulated and calculated as stochastically.

Keywords: ruin probability, quantum mechanics, Hamiltonian technique, operator approach

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Authors: Naoyuki Sugihashi, Toshiharu Kishi

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The probability of occurrence of thermal cracks in mass concrete in Japan is evaluated by the cracking probability diagram that represents the relationship between the thermal cracking index and the probability of occurrence of cracks in the actual structure. In this paper, we propose a method to directly calculate the cracking probability, following a probabilistic theory by modeling the variance of tensile stress and tensile strength. In this method, the relationship between the variance of tensile stress and tensile strength, the thermal cracking index, and the cracking probability are formulated and presented. In addition, standard deviation of tensile stress and tensile strength was identified, and the method of calculating cracking probability in a general construction controlled environment was also demonstrated.

Keywords: thermal crack control, mass concrete, thermal cracking probability, durability of concrete, calculating method of cracking probability

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Authors: Shin-Shin Kao, Yuan-Kang Shih, Hsun Su

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In this paper, we show that the conjecture of Chv tal, which states that any 1-tough graph is either a Hamiltonian graph or its complement contains a specific graph denoted by F, does not hold in general. More precisely, it is true only for graphs with six or seven vertices, and is false for graphs with eight or more vertices. A theorem is derived as a correction for the conjecture.

Keywords: complement, degree sum, hamiltonian, tough

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Authors: Mukunda Upreti, Jill Storry, Rafael Björk, Emilie Louvet, Johan Normark, Sven Bergström

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Borrelia duttonii and most other relapsing fever species are Gram-negative bacteria which cause a blood borne infection characterized by the binding of bacterium to erythrocytes. The bacteria associate with two or more erythrocytes to form clusters of cells into rosettes. Rosetting is a major virulence factor and the mechanism is believed to facilitate persistence of bacteria in the circulatory system and the avoidance of host immune cells through masking or steric hindrance effects. However, the molecular mechanisms of rosette formation are still poorly understood. This study aims at determining the molecules involved in the rosette formation phenomenon. Fractionated serum, using different affinity purification methods, was investigated as a rosetting agent and IgG and at least one other serum components were needed for rosettes to form. An IgG titration curve demonstrated that IgG alone is not enough to restore rosette formation level to the level whole serum gives. IgG hydrolysis by IdeS ( Immunoglobulin G-degrading enzyme of Streptococcus pyogenes) and deglycosylation using N-Glycanase proved that the whole IgG molecule regardless of saccharide moieties is critical for Borrelia induced rosetting. Complement components C3 and C4 were also important serum molecules necessary to maintain optimum rosetting rates. The deactivation of complement network and serum depletion with C3 and C4 significantly reduced the rosette formation rate. The dependency of IgG and complement components also implied involvement of the complement receptor (CR1). Rosette formation test with Knops null RBC and sCR1 confirmed that CR1 is also part of Borrelia induced rosette formation.

Keywords: complement components C3 and C4, complement receptor 1, Immunoglobulin G, Knops null, Rosetting

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Authors: Ahmet Kaya

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Quantum mechanism is one of the most important approaches to calculating non-ruin probability. We apply standard Dirac notation to model given Hamiltonians. By using the traditional method and eigenvector basis, non-ruin probability is found for several examples. Also, non-ruin probability is calculated for two different Hamiltonian by using the tensor product. Finally, the path integral method is applied to the examples and comparison is made for stochastic simulations and path integral calculation.

Keywords: quantum physics, Hamiltonian system, path integral, tensor product, ruin probability

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Authors: Toby Li, Julian Zhu

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In this paper, a model based on a simplified geometry is introduced to give a very conservative collision probability prediction for the Starlink satellite in its most densely clustered region. Under the model in this paper, the probability of collision for Starlink satellite where it clustered most densely is found to be 8.484 ∗ 10^−4. It is found that the predicted collision probability increased nonlinearly with the increased safety distance set. This simple model provides evidence that the continuous development of maneuver avoidance systems is necessary for the future of the orbital safety of satellites under the harsher Lower Earth Orbit environment.

Keywords: Starlink, collision probability, debris, geometry model

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Authors: Jiyoung Yoon

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This study examines Spanish textbook explanations of infinitival complements and how they can affect a learner’s second-language acquisition process. Verbs taking infinitival complements are commonly found in the mandate, volition, and emotion verbs, both for Spanish and English. However, while some English verbs take gerunds (María avoids eating/*to eat meat), in Spanish a gerund never functions as the complement of a verb (María evita comer/*comiendo carne). Because of these differences, English learners of Spanish often have difficulty acquiring infinitival complement constructions in Spanish. Specifically, they may employ English-like complement structures, producing such ungrammatical utterances as *Odio comiendo tacos ‘I hate eating tacos.' A compounding factor is that many Spanish textbooks do not emphasize the usages of infinitival complements and, when explanations are provided, they are often vague and insufficient. This study examines Spanish textbook explanations of infinitival complements (intermediate and advanced college-level Spanish textbooks and grammar reference books published in the United States) to determine areas that are problematic and insufficient and how they can affect learners’ second-language acquisition process. In this study, alternative principle-driven explanations are proposed as a replacement.

Keywords: Spanish, teaching, second language, infinitival complement, textbook

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Authors: Yuan-Lin Chen

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This paper presents an approaching forward collision probability index (AFCPI) for alerting and assisting driver in keeping safety distance to avoid the forward collision accident in highway driving. The time to collision (TTC) and time headway (TH) are used to evaluate the TTC forward collision probability index (TFCPI) and the TH forward collision probability index (HFCPI), respectively. The Mamdani fuzzy inference algorithm is presented combining TFCPI and HFCPI to calculate the approaching collision probability index of the vehicle. The AFCPI is easier to understand for the driver who did not even have any professional knowledge in vehicle professional field. At the same time, the driver’s behavior is taken into account for suiting each driver. For the approaching index, the value 0 is indicating the 0% probability of forward collision, and the values 0.5 and 1 are indicating the 50% and 100% probabilities of forward collision, respectively. The AFCPI is useful and easy-to-understand for alerting driver to avoid the forward collision accidents when driving in highway.

Keywords: approaching index, forward collision probability, time to collision, time headway

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Authors: Karim Hamidi Machekposhti, Hossein Sedghi

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This study was designed to find the best-fit probability distribution of annual rainfall based on 50 years sample (1966-2015) in the Karkheh river basin at Iran using six probability distributions: Normal, 2-Parameter Log Normal, 3-Parameter Log Normal, Pearson Type 3, Log Pearson Type 3 and Gumbel distribution. The best fit probability distribution was selected using Stormwater Management and Design Aid (SMADA) software and based on the Residual Sum of Squares (R.S.S) between observed and estimated values Based on the R.S.S values of fit tests, the Log Pearson Type 3 and then Pearson Type 3 distributions were found to be the best-fit probability distribution at the Jelogir Majin and Pole Zal rainfall gauging station. The annual values of expected rainfall were calculated using the best fit probability distributions and can be used by hydrologists and design engineers in future research at studied region and other region in the world.

Keywords: Log Pearson Type 3, SMADA, rainfall, Karkheh River

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Authors: Komeil Valipourian

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Urban advances and the growing need for developing infrastructures has increased the importance of deep excavations. In this study, after the introducing probability analysis as an important issue, an attempt has been made to apply it for the deep excavation project of Bangkok’s Metro as a case study. For this, the numerical probability model has been developed based on the Finite Difference Method and Monte Carlo sampling approach. The results indicate that disregarding the issue of probability in this project will result in an inappropriate design of the retaining structure. Therefore, probabilistic redesign of the support is proposed and carried out as one of the applications of probability analysis. A 50% reduction in the flexural strength of the structure increases the failure probability just by 8% in the allowable range and helps improve economic conditions, while maintaining mechanical efficiency. With regard to the lack of efficient design in most deep excavations, by considering geometrical and geotechnical variability, an attempt was made to develop an optimum practical design standard for deep excavations based on failure probability. On this basis, a practical relationship is presented for estimating the maximum allowable horizontal displacement, which can help improve design conditions without developing the probability analysis.

Keywords: numerical probability modeling, deep excavation, allowable maximum displacement, finite difference method (FDM)

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Authors: Yuanjin Liu

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Retirement withdrawal strategies are very important to minimize the probability of ruin in retirement. The ruin probability is modeled as a function of initial withdrawal age, gender, asset allocation, inflation rate, and initial withdrawal rate. The ruin probability is obtained based on the 2019 period life table for the Social Security, IRS Required Minimum Distribution (RMD) Worksheets, US historical bond and equity returns, and inflation rates using simulation. Several popular machine learning algorithms of the generalized additive model, random forest, support vector machine, extreme gradient boosting, and artificial neural network are built. The model validation and selection are based on the test errors using hyperparameter tuning and train-test split. The optimal model is recommended for retirees to monitor the ruin probability. The optimal withdrawal strategy can be obtained based on the optimal predictive model.

Keywords: ruin probability, retirement withdrawal strategies, predictive models, optimal model

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Authors: Quznetsov Gunn

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In the study of the logical foundations of probability theory, it was found that the terms and equations of the fundamental theoretical physics represent terms and theorems of the classical probability theory, more precisely, of that part of this theory, which considers the probability of dot events in the 3 + 1 space-time. In particular, the masses, moments, energies, spins, etc. turn out of parameters of probability distributions such events. The terms and the equations of the electroweak and of the quark-gluon theories turn out the theoretical-probabilistic terms and theorems. Here the relation of a neutrino to his lepton becomes clear, the W and Z bosons masses turn out dynamic ones, the cause of the asymmetry between particles and antiparticles is the impossibility of the birth of single antiparticles. In addition, phenomena such as confinement and asymptotic freedom receive their probabilistic explanation. And here we have the logical foundations of the gravity theory with phenomena dark energy and dark matter.

Keywords: classical theory of probability, logical foundation of fundamental theoretical physics, masses, moments, energies, spins

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Authors: Sean Sloan

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Probability Risk Assessments (PRA) can be a difficult concept for students to grasp. So in searching for different ways to describe PRA to relate it to their lives; COVID-19 came up. The parallels are amazing. Soon students began analyzing acceptable risk with the virus. This helped them to quantify just how dangerous is dangerous. The original lesson was dismissed and for the remainder of the period, the probability of risk, and the lethality of risk became the topic. Spreading events such as a COVID carrier on an airline became analogous to single fault casualties such as a Tsunami. Odds of spreading became odds of backup-diesel-generator failure – like with Fukashima Daiichi. Fatalities of the disease became expected fatalities due to radiation spread. Quantification from this discussion took it from hyperbole and emotion into one where we could rationally base guidelines. It has been one of the most effective educational devices observed.

Keywords: COVID, education, probability, risk

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Authors: Sule Sahin, Basak Bulut Karageyik

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This paper introduces a hazard rate function for the time of ruin to calculate the conditional probability of ruin for very small intervals. We call this function the force of ruin (FoR). We obtain the expected time of ruin and conditional expected time of ruin from the exact finite time ruin probability with exponential claim amounts. Then we introduce the FoR which gives the conditional probability of ruin and the condition is that ruin has not occurred at time t. We analyse the behavior of the FoR function for different initial surpluses over a specific time interval. We also obtain FoR under the excess of loss reinsurance arrangement and examine the effect of reinsurance on the FoR.

Keywords: conditional time of ruin, finite time ruin probability, force of ruin, reinsurance

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Authors: Junling Li, Fang Meng, Yichun Zhang

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Image saliency detection has been long studied, while several challenging problems are still unsolved, such as detecting saliency inaccurately in complex scenes or suppressing salient objects in the image borders. In this paper, we propose a new saliency detection algorithm in order to solving these problems. We represent the image as a graph with superixels as nodes. By considering appearance similarity between the boundary and the background, the proposed method chooses non-saliency boundary nodes as background priors to construct the background probability model. The probability that each node belongs to the model is computed, which measures its similarity with backgrounds. Thus we can calculate saliency by the transformed probability as a metric. We compare our algorithm with ten-state-of-the-art salient detection methods on the public database. Experimental results show that our simple and effective approach can attack those challenging problems that had been baffling in image saliency detection.

Keywords: visual saliency, background probability, boundary knowledge, background priors

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Authors: Aleš Florian, Lenka Ševelová, Jaroslav Žák

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Formation of tensile cracks in concrete slabs of rigid pavement can be (among others) the initiation point of the other, more serious failures which can ultimately lead to complete degradation of the concrete slab and thus the whole pavement. Two measures can be used for reliability assessment of this phenomenon - the probability of failure and/or the reliability index. Different methods can be used for their calculation. The simple ones are called moment methods and simulation techniques. Two methods - FOSM Method and Simple Random Sampling Method - are verified and their comparison is performed. The influence of information about the probability distribution and the statistical parameters of input variables as well as of the limit state function on the calculated reliability index and failure probability are studied in three points on the lower surface of concrete slabs of the older type of rigid pavement formerly used in the Czech Republic.

Keywords: failure, pavement, probability, reliability index, simulation, tensile crack

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Authors: Hung-Chieh Chen, Kuo-Hui Wang, Tsu-Lin Yeh

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Proteomics represent the performance of genomic complement proteins and the protein level on functional genomics. This study adopted proteomic strategies for comparing serum proteins among three groups: elite sprinter (sprint runner group, SR), long-distance runners (long-distance runner group, LDR), and the untrained control group (control group, CON). Purposes: This study aims to identify elite sprinters and long-distance runners’ serum protein and to provide a comparison of their serum proteome’ composition. Methods: Serum protein fractionations that separated by sodium dodecyl sulfate-polyacrylamide gel electrophoresis (SDS-PAGE) and analyzed by a quantitative nano-LC-MS/MS-based proteomic profiling. The one-way analysis of variance (ANOVA) and Scheffe post hoc comparison (α= 0.05) was used to determine whether there is any significant difference in each protein level among the three groups. Results: (1) After analyzing the 307 identified proteins, there were 26 unique proteins in the SR group, and 18 unique proteins in the LDR group. (2) For the LDR group, 7 coagulation function-associated proteins’ expression levels were investigated: vitronectin, serum paraoxonase/arylesterase 1, fibulin-1, complement C3, vitamin K-dependent protein, inter-alpha-trypsin inhibitor heavy chain H3 and von Willebrand factor, and the findings show the seven coagulation function-associated proteins were significantly lower than the group of SR. (3) Comparing to the group of SR, this study found that the LDR group’s expression levels of the 2 antioxidant proteins (afamin and glutathione peroxidase 3) were also significantly lower. (4) The LDR group’s expression levels of seven immune function-related proteins (Ig gamma-3 chain C region, Ig lambda-like polypeptide 5, clusterin, complement C1s subcomponent, complement factor B, complement C4-A, complement C1q subcomponent subunit A) were also significantly lower than the group of SR. Conclusion: This study identified the potential serum protein markers for elite sprinters and long-distance runners. The changes in the regulation of coagulation, antioxidant, or immune function-specific proteins may also provide further clinical applications for these two different track athletes.

Keywords: biomarkers, coagulation, immune response, oxidative stress

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Authors: Yasir Alotaibi

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The aim of this paper is to discuss the syntactic analysis of aspectual or phasal verbs in Modern Standard Arabic (MSA). Aspectual or phasal verbs refer to a class of verbs that require a verbal complement and denote the inception, duration, termination ...etc. of a state or event. This paper will discuss two groups of aspectual verbs in MSA. The first group includes verbs such as ̆gacala, tafiqa, ?akhatha, ?ansha?a, sharaca and bada?a and these verbs are used to denote the inception of an event. The second group includes verbs such as ?awshaka, kaada and karaba and the meaning of these verbs is equivalent to be near/almost . The following examples illustrate the use of the verb bada?a ‘begin’ which is from the first group: a. saalim-un bada?a yuthaakiru. Salem-NOM begin.PFV.3SGM study.IPFV.3SGM ‘Salem began to study’ b.*saalim-un bada?a ?an yuthaakiru. Salem-NOM begin.PFV.3SGM COMP study.IPFV.3SGM ‘Salem began to study’ The example in (1a) is grammatical because the aspectual verb is used with a verbal complement that is not introduced by a complementizer. In contrast, example (1b) is not grammatical because the verbal complement is introduced by the complementizer ?an ‘that’. In contrast, the following examples illustrate the use of the verb kaada ‘be almost’ which is from the second group. However, the two examples are grammatical and this means that the verbal complement of this verb can be without (as in example (2a)) or with ( as in example (2b)) a complementizer. (2) a. saalim-un kaada yuthaakiru. Salem-NOM be.almost.PFV.3SGM study.IPFV.3SGM ‘Salem was almost to study’ b. saalim-un kaada ?an yuthaakiru. Salem-NOM be.almost.PFV.3SGM COMP study.IPFV.3SGM ‘Salem was almost to study’ The salient properties of this class of verbs are that they require a verbal complement, there is no a complementizer that can introduce the complement with the first group while it is possible with the second and the aspectual verb and the embedded verb share and agree with the same subject. To the best of knowledge, aspectual verbs in MSA are discussed in traditional grammar only and have not been studied in modern syntactic theories. This paper will consider the analysis of aspectual verbs in MSA within the Lexical Functional Grammar (LFG) framework. It will use some evidence such as modifier or negation to find out whether these verbs have PRED values and head their f-structures or they form complex predicates with their complements. If aspectual verbs show the properties of heads, then the paper will explore what kind of heads they are. In particular, they should be raising or control verbs. The paper will use some tests such as agreement, selectional restrictions...etc. to find out what kind of verbs they are.

Keywords: aspectual verbs, biclausal, monoclausal, raising

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Authors: Jerry Hu

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Let G = (V, E) with V = {1, 2, ..., k} be a graph, the k positive integers a₁, a₂, ..., ak are G-wise relatively prime if (aᵢ, aⱼ ) = 1 for {i, j} ∈ E. We use an inductive approach to give an asymptotic formula for the number of k-tuples of integers that are G-wise relatively prime. An exact formula is obtained for the probability that k positive integers are G-wise relatively prime. As a corollary, we also provide an exact formula for the probability that k positive integers have exactly r relatively prime pairs.

Keywords: graph, independent set, G-wise relatively prime, probability

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Authors: Bahareh Zare

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The theory of the investment model of dating infidelity maintains that loyalty is an essential power within romantic relationships. Loyalty signifies both motivation and psychological attachment to maintain a relationship. This study examined the relationship between the Big Five Personality Factors (Extraversion, Neuroticism, Openness, Conscientiousness, and Agreeableness), probability of marital infidelity, and risk of divorce. The participants completed NEO-FFI, INFQ (infidelity questionnaire) and were interviewed by OHI (Oral History Interview). The results demonstrated that extraversion and agreeableness traits were significant predictors for the probability of infidelity and risk of divorce. In addition, conscientiousness predicted the probability of infidelity, while neuroticism predicted the risk of divorce.

Keywords: five factors personality, infidelity, risk of divorce, investment theory

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Authors: Seon Soon Choi

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The fatigue crack growth is stochastic because of the fatigue behavior having an uncertainty and a randomness. Therefore, it is necessary to determine the probability distribution of a grown crack size at a specific fatigue crack propagation life for maintenance of structure as well as reliability estimation. The essential purpose of this study is to present the good probability distribution fit for the grown crack size at a specified fatigue life in a rolled magnesium alloy under different specimen thickness conditions. Fatigue crack propagation experiments are carried out in laboratory air under three conditions of specimen thickness using AZ31 to investigate a stochastic crack growth behavior. The goodness-of-fit test for probability distribution of a grown crack size under different specimen thickness conditions is performed by Anderson-Darling test. The effect of a specimen thickness on variability of a grown crack size is also investigated.

Keywords: crack size, fatigue crack propagation, magnesium alloys, probability distribution, specimen thickness

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Authors: Mohd Aftar Abu Bakar, Noratiqah Mohd Ariff, Abdul Aziz Jemain

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Storm Event Analysis (SEA) provides a method to define rainfalls events as storms where each storm has its own amount and duration. By modelling daily probability of different types of storms, the onset, offset and cycle of rainfall seasons can be determined and investigated. Furthermore, researchers from the field of meteorology will be able to study the dynamical characteristics of rainfalls and make predictions for future reference. In this study, four categories of storms; short, intermediate, long and very long storms; are introduced based on the length of storm duration. Daily probability models of storms are built for these four categories of storms in Peninsular Malaysia. The models are constructed by using Bernoulli distribution and by applying linear regression on the first Fourier harmonic equation. From the models obtained, it is found that daily probability of storms at the Eastern part of Peninsular Malaysia shows a unimodal pattern with high probability of rain beginning at the end of the year and lasting until early the next year. This is very likely due to the Northeast monsoon season which occurs from November to March every year. Meanwhile, short and intermediate storms at other regions of Peninsular Malaysia experience a bimodal cycle due to the two inter-monsoon seasons. Overall, these models indicate that Peninsular Malaysia can be divided into four distinct regions based on the daily pattern for the probability of various storm events.

Keywords: daily probability model, monsoon seasons, regions, storm events

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Authors: Suparat Niwitpong, Sa-aat Niwitpong

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Statistical inference of normal mean with known coefficient of variation has been investigated recently. This phenomenon occurs normally in environment and agriculture experiments when the scientist knows the coefficient of variation of their experiments. In this paper, we constructed new confidence intervals for the normal population mean with known coefficient of variation. We also derived analytic expressions for the coverage probability of each confidence interval. To confirm our theoretical results, Monte Carlo simulation will be used to assess the performance of these intervals based on their coverage probabilities.

Keywords: confidence interval, coverage probability, expected length, known coefficient of variation

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Authors: Seon Soon Choi

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It is necessary to predict a fatigue crack propagation life for estimation of structural integrity. Because of an uncertainty and a randomness of a structural behavior, it is also required to analyze stochastic characteristics of the fatigue crack propagation life at a specified fatigue crack size. The essential purpose of this study is to present the good probability distribution fit for the fatigue crack propagation life at a specified fatigue crack size in magnesium alloys under various fatigue load ratio conditions. To investigate a stochastic crack growth behavior, fatigue crack propagation experiments are performed in laboratory air under several conditions of fatigue load ratio using AZ31. By Anderson-Darling test, a goodness-of-fit test for probability distribution of the fatigue crack propagation life is performed and the good probability distribution fit for the fatigue crack propagation life is presented. The effect of load ratio on variability of fatigue crack propagation life is also investigated.

Keywords: fatigue crack propagation life, load ratio, magnesium alloys, probability distribution

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Authors: Mohammed A. Hajeeh

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This paper examines the behavior of a system, which upon failure is either replaced with certain probability p or imperfectly repaired with probability q. The system is analyzed using Kolmogorov's forward equations method; the analytical expression for the steady state availability is derived as an indicator of the system’s performance. It is found that the analysis becomes more complex as the number of imperfect repairs increases. It is also observed that the availability increases as the number of states and replacement probability increases. Using such an approach in more complex configurations and in dynamic systems is cumbersome; therefore, it is advisable to resort to simulation or heuristics. In this paper, an example is provided for demonstration.

Keywords: repairable models, imperfect, availability, exponential distribution

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Authors: Julio Vicente Cateia

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This paper aims to assess the role of informality and trade facilitation on the export probability of Guinea-Bissau. We include informality in the Féchet function, which gives the expression for the country's supply probability. We find that Guinea-Bissau is about 7.2% less likely to export due to the 1% increase in informality. The export's probability increases by about 1.7%, 4%, and 1.1% due to a 1% increase in trade facilitation, R&D stock, and year of education. These results are significant at the usual levels. We suggest a development agenda aimed at reducing the level of informality in this country.

Keywords: development, trade, informality, trade facilitation, economy of Guinea-Bissau

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Authors: Tomoaki Hashimoto

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In recent decades, probabilistic constrained optimal control problems have attracted much attention in many research field. Although probabilistic constraints are generally intractable in an optimization problem, several tractable methods haven been proposed to handle probabilistic constraints. In most methods, probabilistic constraints are reduced to deterministic constraints that are tractable in an optimization problem. However, there is a gap between the transformed deterministic constraints in case of known and unknown probability distribution. This paper examines the conservativeness of probabilistic constrained optimization method with the unknown probability distribution. The objective of this paper is to provide a quantitative assessment of the conservatism for tractable constraints in probabilistic constrained optimization with the unknown probability distribution.

Keywords: optimal control, stochastic systems, discrete time systems, probabilistic constraints

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