Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 5530

Search results for: possibility distribution

5530 Parameters Estimation of Multidimensional Possibility Distributions

Authors: Sergey Sorokin, Irina Sorokina, Alexander Yazenin

Abstract:

We present a solution to the Maxmin u/E parameters estimation problem of possibility distributions in m-dimensional case. Our method is based on geometrical approach, where minimal area enclosing ellipsoid is constructed around the sample. Also we demonstrate that one can improve results of well-known algorithms in fuzzy model identification task using Maxmin u/E parameters estimation.

Keywords: possibility distribution, parameters estimation, Maxmin u\E estimator, fuzzy model identification

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5529 A Proposed Mechanism for Skewing Symmetric Distributions

Authors: M. T. Alodat

Abstract:

In this paper, we propose a mechanism for skewing any symmetric distribution. The new distribution is called the deflation-inflation distribution (DID). We discuss some statistical properties of the DID such moments, stochastic representation, log-concavity. Also we fit the distribution to real data and we compare it to normal distribution and Azzlaini's skew normal distribution. Numerical results show that the DID fits the the tree ring data better than the other two distributions.

Keywords: normal distribution, moments, Fisher information, symmetric distributions

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5528 Prediction of Product Size Distribution of a Vertical Stirred Mill Based on Breakage Kinetics

Authors: C. R. Danielle, S. Erik, T. Patrick, M. Hugh

Abstract:

In the last decade there has been an increase in demand for fine grinding due to the depletion of coarse-grained orebodies and an increase of processing fine disseminated minerals and complex orebodies. These ores have provided new challenges in concentrator design because fine and ultra-fine grinding is required to achieve acceptable recovery rates. Therefore, the correct design of a grinding circuit is important for minimizing unit costs and increasing product quality. The use of ball mills for grinding in fine size ranges is inefficient and, therefore, vertical stirred grinding mills are becoming increasingly popular in the mineral processing industry due to its already known high energy efficiency. This work presents a hypothesis of a methodology to predict the product size distribution of a vertical stirred mill using a Bond ball mill. The Population Balance Model (PBM) was used to empirically analyze the performance of a vertical mill and a Bond ball mill. The breakage parameters obtained for both grinding mills are compared to determine the possibility of predicting the product size distribution of a vertical mill based on the results obtained from the Bond ball mill. The biggest advantage of this methodology is that most of the minerals processing laboratories already have a Bond ball mill to perform the tests suggested in this study. Preliminary results show the possibility of predicting the performance of a laboratory vertical stirred mill using a Bond ball mill.

Keywords: bond ball mill, population balance model, product size distribution, vertical stirred mill

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5527 Evaluating the Possibility of Expanding National Health Insurance Funding From Zakat, Sudan

Authors: Fawzia Mohammed Idris

Abstract:

Zakat is an Islamic procedure for wealth distribution as a social protection mechanism for needy people. This study aimed to assess the possibility to expand the share of fund for national health insurance fund from zakat funds allocated for poor people by measuring the reduction of poverty that result from the investing on direct payment to the needy or by covering them in social health insurance. This study used stata regression as a statistical analysis tool and the finding clarified that there is no significant relationship between the poverty rate as the main indicator and, the number of poor people covered by national health insurance on one hand and the number of benefits poor people from the distribution of zakat fund. This study experienced many difficulties regarding the quality and the consistency of the data. The study suggested that a joint mission between national health insurance fund and zakat chamber to conduct study to assess the efficient use of zakat fund allocated to poor people.

Keywords: health finance, poverty, social health insurance, zakat

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5526 A Flexible Pareto Distribution Using α-Power Transformation

Authors: Shumaila Ehtisham

Abstract:

In Statistical Distribution Theory, considering an additional parameter to classical distributions is a usual practice. In this study, a new distribution referred to as α-Power Pareto distribution is introduced by including an extra parameter. Several properties of the proposed distribution including explicit expressions for the moment generating function, mode, quantiles, entropies and order statistics are obtained. Unknown parameters have been estimated by using maximum likelihood estimation technique. Two real datasets have been considered to examine the usefulness of the proposed distribution. It has been observed that α-Power Pareto distribution outperforms while compared to different variants of Pareto distribution on the basis of model selection criteria.

Keywords: α-power transformation, maximum likelihood estimation, moment generating function, Pareto distribution

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5525 An Extension of the Generalized Extreme Value Distribution

Authors: Serge Provost, Abdous Saboor

Abstract:

A q-analogue of the generalized extreme value distribution which includes the Gumbel distribution is introduced. The additional parameter q allows for increased modeling flexibility. The resulting distribution can have a finite, semi-infinite or infinite support. It can also produce several types of hazard rate functions. The model parameters are determined by making use of the method of maximum likelihood. It will be shown that it compares favourably to three related distributions in connection with the modeling of a certain hydrological data set.

Keywords: extreme value theory, generalized extreme value distribution, goodness-of-fit statistics, Gumbel distribution

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5524 Self-Action of Pyroelectric Spatial Soliton in Undoped Lithium Niobate Samples with Pyroelectric Mechanism of Nonlinear Response

Authors: Anton S. Perin, Vladimir M. Shandarov

Abstract:

Compensation for the nonlinear diffraction of narrow laser beams with wavelength of 532 and the formation of photonic waveguides and waveguide circuits due to the contribution of pyroelectric effect to the nonlinear response of lithium niobate crystal have been experimentally demonstrated. Complete compensation for the linear and nonlinear diffraction broadening of light beams is obtained upon uniform heating of an undoped sample from room temperature to 55 degrees Celsius. An analysis of the light-field distribution patterns and the corresponding intensity distribution profiles allowed us to estimate the spacing for the channel waveguides. The observed behavior of bright soliton beams may be caused by their coherent interaction, which manifests itself in repulsion for anti-phase light fields and in attraction for in-phase light fields. The experimental results of this study showed a fundamental possibility of forming optically complex waveguide structures in lithium niobate crystals with pyroelectric mechanism of nonlinear response. The topology of these structures is determined by the light field distribution on the input face of crystalline sample. The optical induction of channel waveguide elements by interacting spatial solitons makes it possible to design optical systems with a more complex topology and a possibility of their dynamic reconfiguration.

Keywords: self-action, soliton, lithium niobate, piroliton, photorefractive effect, pyroelectric effect

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5523 Loss Analysis by Loading Conditions of Distribution Transformers

Authors: A. Bozkurt, C. Kocatepe, R. Yumurtaci, İ. C. Tastan, G. Tulun

Abstract:

Efficient use of energy, with the increase in demand of energy and also with the reduction of natural energy sources, has improved its importance in recent years. Most of the losses in the system from electricity produced until the point of consumption is mostly composed by the energy distribution system. In this study, analysis of the resulting loss in power distribution transformer and distribution power cable is realized which are most of the losses in the distribution system. Transformer losses in the real distribution system were analyzed by CYME Power Engineering Software program. These losses are disclosed for different voltage levels and different loading conditions.

Keywords: distribution system, distribution transformer, power cable, technical losses

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5522 Particle Size Distribution Estimation of a Mixture of Regular and Irregular Sized Particles Using Acoustic Emissions

Authors: Ejay Nsugbe, Andrew Starr, Ian Jennions, Cristobal Ruiz-Carcel

Abstract:

This works investigates the possibility of using Acoustic Emissions (AE) to estimate the Particle Size Distribution (PSD) of a mixture of particles that comprise of particles of different densities and geometry. The experiments carried out involved the mixture of a set of glass and polyethylene particles that ranged from 150-212 microns and 150-250 microns respectively and an experimental rig that allowed the free fall of a continuous stream of particles on a target plate which the AE sensor was placed. By using a time domain based multiple threshold method, it was observed that the PSD of the particles in the mixture could be estimated.

Keywords: acoustic emissions, particle sizing, process monitoring, signal processing

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5521 Exponentiated Transmuted Weibull Distribution: A Generalization of the Weibull Probability Distribution

Authors: Abd El Hady N. Ebraheim

Abstract:

This paper introduces a new generalization of the two parameter Weibull distribution. To this end, the quadratic rank transmutation map has been used. This new distribution is named exponentiated transmuted Weibull (ETW) distribution. The ETW distribution has the advantage of being capable of modeling various shapes of aging and failure criteria. Furthermore, eleven lifetime distributions such as the Weibull, exponentiated Weibull, Rayleigh and exponential distributions, among others follow as special cases. The properties of the new model are discussed and the maximum likelihood estimation is used to estimate the parameters. Explicit expressions are derived for the quantiles. The moments of the distribution are derived, and the order statistics are examined.

Keywords: exponentiated, inversion method, maximum likelihood estimation, transmutation map

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5520 The Beta-Fisher Snedecor Distribution with Applications to Cancer Remission Data

Authors: K. A. Adepoju, O. I. Shittu, A. U. Chukwu

Abstract:

In this paper, a new four-parameter generalized version of the Fisher Snedecor distribution called Beta- F distribution is introduced. The comprehensive account of the statistical properties of the new distributions was considered. Formal expressions for the cumulative density function, moments, moment generating function and maximum likelihood estimation, as well as its Fisher information, were obtained. The flexibility of this distribution as well as its robustness using cancer remission time data was demonstrated. The new distribution can be used in most applications where the assumption underlying the use of other lifetime distributions is violated.

Keywords: fisher-snedecor distribution, beta-f distribution, outlier, maximum likelihood method

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5519 On Flow Consolidation Modelling in Urban Congested Areas

Authors: Serban Stere, Stefan Burciu

Abstract:

The challenging and continuously growing competition in the urban freight transport market emphasizes the need for optimal planning of transportation processes in terms of identifying the solution of consolidating traffic flows in congested urban areas. The aim of the present paper is to present the mathematical framework and propose a methodology of combining urban traffic flows between the distribution centers located at the boundary of a congested urban area. The three scenarios regarding traffic flow between consolidation centers that are taken into consideration in the paper are based on the same characteristics of traffic flows. The scenarios differ in terms of the accessibility of the four consolidation centers given by the infrastructure, the connections between them, and the possibility of consolidating traffic flows for one or multiple destinations. Also, synthetical indicators will allow us to compare the scenarios considered and chose the indicated for our distribution system.

Keywords: distribution system, single and multiple destinations, urban consolidation centers, traffic flow consolidation schemes

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5518 Efficient Design of Distribution Logistics by Using a Model-Based Decision Support System

Authors: J. Becker, R. Arnold

Abstract:

The design of distribution logistics has a decisive impact on a company's logistics costs and performance. Hence, such solutions make an essential contribution to corporate success. This article describes a decision support system for analyzing the potential of distribution logistics in terms of logistics costs and performance. In contrast to previous procedures of business process re-engineering (BPR), this method maps distribution logistics holistically under variable distribution structures. Combined with qualitative measures the decision support system will contribute to a more efficient design of distribution logistics.

Keywords: decision support system, distribution logistics, potential analyses, supply chain management

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5517 Design of Distribution Network for Gas Cylinders in Jordan

Authors: Hazem J. Smadi

Abstract:

Performance of a supply chain is directly related to a distribution network that entails the location of storing materials or products and how products are delivered to the end customer through different stages in the supply chain. This study analyses the current distribution network used for delivering gas cylinders to end customer in Jordan. Evaluation of current distribution has been conducted across customer service components. A modification on the current distribution network in terms of central warehousing in each city in the country improves the response time and customer experience. 

Keywords: distribution network, gas cylinder, Jordan, supply chain

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5516 A New Distribution and Application on the Lifetime Data

Authors: Gamze Ozel, Selen Cakmakyapan

Abstract:

We introduce a new model called the Marshall-Olkin Rayleigh distribution which extends the Rayleigh distribution using Marshall-Olkin transformation and has increasing and decreasing shapes for the hazard rate function. Various structural properties of the new distribution are derived including explicit expressions for the moments, generating and quantile function, some entropy measures, and order statistics are presented. The model parameters are estimated by the method of maximum likelihood and the observed information matrix is determined. The potentiality of the new model is illustrated by means of real life data set.

Keywords: Marshall-Olkin distribution, Rayleigh distribution, estimation, maximum likelihood

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5515 The Current Situation of Ang Thong Province’s Court Doll Distribution

Authors: Phutthiwat Waiyawuththanapoom

Abstract:

This research is objected to study the pattern and channel of distribution of Ang Thong’s court doll OTOP product and try to develop the quality of distribution of the court doll product. The population of this research is 50 court doll manufacturers of Ang Thong’s court doll. The data and information was collected by using the questionnaire and use percentage, mean and standard deviation as an analysis tools. The distribution channel of Ang Thong’s court doll can be separated into 3 channels which are direct distribution from the manufacturer, via the middleman and via the co-operated manufacturing group. In the direct distribution from the manufacturer channel, it was found that the manufacturer is given the highest rate of importance to how they keep the inventory. In the distribution via the middleman channel, it was found that the manufacturer is given the highest rate of importance to the distribution efficiency. But in the distribution via the co-operated manufacturing group, it was found that the manufacturer is given the highest rate of importance to the public relationship.

Keywords: distribution, court doll, Ang Thong province, business and social sciences

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5514 Application of Hyperbinomial Distribution in Developing a Modified p-Chart

Authors: Shourav Ahmed, M. Gulam Kibria, Kais Zaman

Abstract:

Control charts graphically verify variation in quality parameters. Attribute type control charts deal with quality parameters that can only hold two states, e.g., good or bad, yes or no, etc. At present, p-control chart is most commonly used to deal with attribute type data. In construction of p-control chart using binomial distribution, the value of proportion non-conforming must be known or estimated from limited sample information. As the probability distribution of fraction non-conforming (p) is considered in hyperbinomial distribution unlike a constant value in case of binomial distribution, it reduces the risk of false detection. In this study, a statistical control chart is proposed based on hyperbinomial distribution when prior estimate of proportion non-conforming is unavailable and is estimated from limited sample information. We developed the control limits of the proposed modified p-chart using the mean and variance of hyperbinomial distribution. The proposed modified p-chart can also utilize additional sample information when they are available. The study also validates the use of modified p-chart by comparing with the result obtained using cumulative distribution function of hyperbinomial distribution. The study clearly indicates that the use of hyperbinomial distribution in construction of p-control chart yields much accurate estimate of quality parameters than using binomial distribution.

Keywords: binomial distribution, control charts, cumulative distribution function, hyper binomial distribution

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5513 A Study on Solutions to Connect Distribution Power Grid up to Renewable Energy Sources at KEPCO

Authors: Seung Yoon Hyun, Hyeong Seung An, Myeong Ho Choi, Sung Hwan Bae, Yu Jong Sim

Abstract:

In 2015, the southern part of the Korean Peninsula has 8.6 million poles, 1.25 million km power lines, and 2 million transformers, etc. It is the massive amount of distribution equipments which could cover a round-trip distance from the earth to the moon and 11 turns around the earth. These distribution equipments are spread out like capillaries and supplying power to every corner of the Korean Peninsula. In order to manage these huge power facility efficiently, KEPCO use DAS (Distribution Automation System) to operate distribution power system since 1997. DAS is integrated system that enables to remotely supervise and control breakers and switches on distribution network. Using DAS, we can reduce outage time and power loss. KEPCO has about 160,000 switches, 50%(about 80,000) of switches are automated, and 41 distribution center monitoring&control these switches 24-hour 365 days to get the best efficiency of distribution networks. However, the rapid increasing renewable energy sources become the problem in the efficient operation of distributed power system. (currently 2,400 MW, 75,000 generators operate in distribution power system). In this paper, it suggests the way to interconnect between renewable energy source and distribution power system.

Keywords: distribution, renewable, connect, DAS (Distribution Automation System)

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5512 Cooling Profile Analysis of Hot Strip Coil Using Finite Volume Method

Authors: Subhamita Chakraborty, Shubhabrata Datta, Sujay Kumar Mukherjea, Partha Protim Chattopadhyay

Abstract:

Manufacturing of multiphase high strength steel in hot strip mill have drawn significant attention due to the possibility of forming low temperature transformation product of austenite under continuous cooling condition. In such endeavor, reliable prediction of temperature profile of hot strip coil is essential in order to accesses the evolution of microstructure at different location of hot strip coil, on the basis of corresponding Continuous Cooling Transformation (CCT) diagram. Temperature distribution profile of the hot strip coil has been determined by using finite volume method (FVM) vis-à-vis finite difference method (FDM). It has been demonstrated that FVM offer greater computational reliability in estimation of contact pressure distribution and hence the temperature distribution for curved and irregular profiles, owing to the flexibility in selection of grid geometry and discrete point position, Moreover, use of finite volume concept allows enforcing the conservation of mass, momentum and energy, leading to enhanced accuracy of prediction.

Keywords: simulation, modeling, thermal analysis, coil cooling, contact pressure, finite volume method

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5511 Water Distribution Uniformity of Solid-Set Sprinkler Irrigation under Low Operating Pressure

Authors: Manal Osman

Abstract:

Sprinkler irrigation system became more popular to reduce water consumption and increase irrigation efficiency. The water distribution uniformity plays an important role in the performance of the sprinkler irrigation system. The use of low operating pressure instead of high operating pressure can be achieved many benefits including energy and water saving. An experimental study was performed to investigate the water distribution uniformity of the solid-set sprinkler irrigation system under low operating pressure. Different low operating pressures (62, 82, 102 and 122 kPa) were selected. The range of operating pressure was lower than the recommended in the previous studies to investigate the effect of low pressure on the water distribution uniformity. Different nozzle diameters (4, 5, 6 and 7 mm) were used. The outdoor single sprinkler test was performed. The water distribution of single sprinkler, the coefficients of uniformity such as coefficient of uniformity (CU), distribution uniformity of low quarter (DUlq), distribution uniformity of low half (DUlh), coefficient of variation (CV) and the distribution characteristics like rotation speed, throw radius and overlapping distance are presented in this paper.

Keywords: low operating pressure, sprinkler irrigation system, water distribution uniformity

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5510 Investigation into the Possibility of Using Recycled Polyethelene to Replace Natural Rubber in the Production of Different Products

Authors: Otokiti Mojeed Jimoh

Abstract:

This work investigates the possibility of using recycled polyethylene LDPE as a base polymer in production of different products (shoe sole, foot mat, and many more) using carbon black as a filler to improve its mechanical properties, like hardness, tensile stress properties and elongation at break properties, from the result so far gotten there is a possibility that there is an increase in the mechanical properties of the sample compare to natural rubber sample.

Keywords: recycled polyethylene, base polymer, hardness, stress properties

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5509 Fault Location Detection in Active Distribution System

Authors: R. Rezaeipour, A. R. Mehrabi

Abstract:

Recent increase of the DGs and microgrids in distribution systems, disturbs the tradition structure of the system. Coordination between protection devices in such a system becomes the concern of the network operators. This paper presents a new method for fault location detection in the active distribution networks, independent of the fault type or its resistance. The method uses synchronized voltage and current measurements at the interconnection of DG units and is able to adapt to changes in the topology of the system. The method has been tested on a 38-bus distribution system, with very encouraging results.

Keywords: fault location detection, active distribution system, micro grids, network operators

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5508 The Effect of Human Capital and Oil Revenue on Income Distribution in Real Sample

Authors: Marjan Majdi, MohammadAli Moradi, Elham Samarikhalaj

Abstract:

Income distribution is one of the most topics in macro economic theories. There are many categories in economy such as income distribution that have the most influenced by economic policies. Human capital has an impact on economic growth and it has significant effect on income distributions. The results of this study confirm that the effects of oil revenue and human capital on income distribution are negative and significant but the value of the estimated coefficient is too small in a real sample in period time (1969-2006).

Keywords: gini coefficient, human capital, income distribution, oil revenue

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5507 Impact of HLA-C*03:04 Allele Frequency Screening Test in Preventing Dapsone-induced SCARs in Thais

Authors: Pear-Rarin Leelakunakorn, Patompong Satapornpong

Abstract:

Introduction: Dapsone is an anti-inflammatory and antibiotic drug that was widely used for the treatment of leprosy, acne fulminans, and dermatitis herpetiformis (DH). However, dapsone is the main cause that triggers severe cutaneous adverse reactions (SCARs), with a possibility of 0.4 to 3.6% of patients after initiating treatment. In fact, the mortality rate of dapsone-induced SCARs is approximately 9.9%. In previous studies, HLA-B*13:01 was strongly associated with dapsone-induced SCARs in Han Chinese, Thais, and Koreans. Nevertheless, the distribution of HLA-B*13:01 marker in each population might differ. Moreover, there were found that the association between HLA-C*03:04 and dapsone hypersensitivity syndrome in Han Chinese leprosy patients by OR = 9.00 and p-value = 2.23×10⁻¹⁹. Objective: The aim of this study was to investigate the distribution of HLA-C* 03:04 in Thailand's healthy population. Method: A total of 350 participants were HLA-C genotyping used sequence-specific oligonucleotides (PCR-SSOs). This study was approved by the Ethics Committee of Rangsit University Result : The most frequency of HLA -C alleles in Thais, consist of HLA -C* 01:02 (17.00 %), -C*08:01 (11.00%) , -C*07:02 (10.70%) , -C* 03:04 ( 9.10%) , -C* 03:02 (8.00%) , -C* 07:01 (6.30%), -C* 07:04 (4.60%), -C* 04:01 (4.40%) ,-C* 12:02 ( 4.30% ) ,and -C* 04:03(3.90%). Interestingly, HLA -C* 03:04 allele was similar to the distribution among Thais and other populations such as Eastern Europe (6.09%), Vietnam (7.42% ), East Croatia (2.25%), and Han Chinese (11.70%). Conclusion: Consequently, HLA-C*03:04 might serve as a pharmacogenetic marker for screening prior to initiation therapy with dapsone for prevention of dapsone-induced SCARs in Thai population.

Keywords: HLA-C*03:04, SCARs, thai population, allele frequency

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5506 Reliability Analysis in Power Distribution System

Authors: R. A. Deshpande, P. Chandhra Sekhar, V. Sankar

Abstract:

In this paper, we discussed the basic reliability evaluation techniques needed to evaluate the reliability of distribution systems which are applied in distribution system planning and operation. Basically, the reliability study can also help to predict the reliability performance of the system after quantifying the impact of adding new components to the system. The number and locations of new components needed to improve the reliability indices to certain limits are identified and studied.

Keywords: distribution system, reliability indices, urban feeder, rural feeder

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5505 Novel Inference Algorithm for Gaussian Process Classification Model with Multiclass and Its Application to Human Action Classification

Authors: Wanhyun Cho, Soonja Kang, Sangkyoon Kim, Soonyoung Park

Abstract:

In this paper, we propose a novel inference algorithm for the multi-class Gaussian process classification model that can be used in the field of human behavior recognition. This algorithm can drive simultaneously both a posterior distribution of a latent function and estimators of hyper-parameters in a Gaussian process classification model with multi-class. Our algorithm is based on the Laplace approximation (LA) technique and variational EM framework. This is performed in two steps: called expectation and maximization steps. First, in the expectation step, using the Bayesian formula and LA technique, we derive approximately the posterior distribution of the latent function indicating the possibility that each observation belongs to a certain class in the Gaussian process classification model. Second, in the maximization step, using a derived posterior distribution of latent function, we compute the maximum likelihood estimator for hyper-parameters of a covariance matrix necessary to define prior distribution for latent function. These two steps iteratively repeat until a convergence condition satisfies. Moreover, we apply the proposed algorithm with human action classification problem using a public database, namely, the KTH human action data set. Experimental results reveal that the proposed algorithm shows good performance on this data set.

Keywords: bayesian rule, gaussian process classification model with multiclass, gaussian process prior, human action classification, laplace approximation, variational EM algorithm

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5504 Modeling the Current and Future Distribution of Anthus Pratensis under Climate Change

Authors: Zahira Belkacemi

Abstract:

One of the most important tools in conservation biology is information on the geographic distribution of species and the variables determining those patterns. In this study, we used maximum-entropy niche modeling (Maxent) to predict the current and future distribution of Anthus pratensis using climatic variables. The results showed that the species would not be highly affected by the climate change in shifting its distribution; however, the results of this study should be improved by taking into account other predictors, and that the NATURA 2000 protected sites will be efficient at 42% in protecting the species.

Keywords: anthus pratensis, climate change, Europe, species distribution model

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5503 Classical and Bayesian Inference of the Generalized Log-Logistic Distribution with Applications to Survival Data

Authors: Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa

Abstract:

A generalized log-logistic distribution with variable shapes of the hazard rate was introduced and studied, extending the log-logistic distribution by adding an extra parameter to the classical distribution, leading to greater flexibility in analysing and modeling various data types. The proposed distribution has a large number of well-known lifetime special sub-models such as; Weibull, log-logistic, exponential, and Burr XII distributions. Its basic mathematical and statistical properties were derived. The method of maximum likelihood was adopted for estimating the unknown parameters of the proposed distribution, and a Monte Carlo simulation study is carried out to assess the behavior of the estimators. The importance of this distribution is that its tendency to model both monotone (increasing and decreasing) and non-monotone (unimodal and bathtub shape) or reversed “bathtub” shape hazard rate functions which are quite common in survival and reliability data analysis. Furthermore, the flexibility and usefulness of the proposed distribution are illustrated in a real-life data set and compared to its sub-models; Weibull, log-logistic, and BurrXII distributions and other parametric survival distributions with 3-parmaeters; like the exponentiated Weibull distribution, the 3-parameter lognormal distribution, the 3- parameter gamma distribution, the 3-parameter Weibull distribution, and the 3-parameter log-logistic (also known as shifted log-logistic) distribution. The proposed distribution provided a better fit than all of the competitive distributions based on the goodness-of-fit tests, the log-likelihood, and information criterion values. Finally, Bayesian analysis and performance of Gibbs sampling for the data set are also carried out.

Keywords: hazard rate function, log-logistic distribution, maximum likelihood estimation, generalized log-logistic distribution, survival data, Monte Carlo simulation

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5502 Constructing the Joint Mean-Variance Regions for Univariate and Bivariate Normal Distributions: Approach Based on the Measure of Cumulative Distribution Functions

Authors: Valerii Dashuk

Abstract:

The usage of the confidence intervals in economics and econometrics is widespread. To be able to investigate a random variable more thoroughly, joint tests are applied. One of such examples is joint mean-variance test. A new approach for testing such hypotheses and constructing confidence sets is introduced. Exploring both the value of the random variable and its deviation with the help of this technique allows checking simultaneously the shift and the probability of that shift (i.e., portfolio risks). Another application is based on the normal distribution, which is fully defined by mean and variance, therefore could be tested using the introduced approach. This method is based on the difference of probability density functions. The starting point is two sets of normal distribution parameters that should be compared (whether they may be considered as identical with given significance level). Then the absolute difference in probabilities at each 'point' of the domain of these distributions is calculated. This measure is transformed to a function of cumulative distribution functions and compared to the critical values. Critical values table was designed from the simulations. The approach was compared with the other techniques for the univariate case. It differs qualitatively and quantitatively in easiness of implementation, computation speed, accuracy of the critical region (theoretical vs. real significance level). Stable results when working with outliers and non-normal distributions, as well as scaling possibilities, are also strong sides of the method. The main advantage of this approach is the possibility to extend it to infinite-dimension case, which was not possible in the most of the previous works. At the moment expansion to 2-dimensional state is done and it allows to test jointly up to 5 parameters. Therefore the derived technique is equivalent to classic tests in standard situations but gives more efficient alternatives in nonstandard problems and on big amounts of data.

Keywords: confidence set, cumulative distribution function, hypotheses testing, normal distribution, probability density function

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5501 Applying the Crystal Model Approach on Light Nuclei for Calculating Radii and Density Distribution

Authors: A. Amar

Abstract:

A new model, namely the crystal model, has been modified to calculate the radius and density distribution of light nuclei up to ⁸Be. The crystal model has been modified according to solid-state physics, which uses the analogy between nucleon distribution and atoms distribution in the crystal. The model has analytical analysis to calculate the radius where the density distribution of light nuclei has obtained from analogy of crystal lattice. The distribution of nucleons over crystal has been discussed in a general form. The equation that has been used to calculate binding energy was taken from the solid-state model of repulsive and attractive force. The numbers of the protons were taken to control repulsive force, where the atomic number was responsible for the attractive force. The parameter has been calculated from the crystal model was found to be proportional to the radius of the nucleus. The density distribution of light nuclei was taken as a summation of two clusters distribution as in ⁶Li=alpha+deuteron configuration. A test has been done on the data obtained for radius and density distribution using double folding for d+⁶,⁷Li with M3Y nucleon-nucleon interaction. Good agreement has been obtained for both the radius and density distribution of light nuclei. The model failed to calculate the radius of ⁹Be, so modifications should be done to overcome discrepancy.

Keywords: nuclear physics, nuclear lattice, study nucleus as crystal, light nuclei till to ⁸Be

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