Search results for: Probability of outage

Authors: Zhanli Zhang, Wei Chen, Xin Jiang, Lili Ma, Shaoting Tang, Zhiming Zheng

Abstract:

A new class of percolation model in complex networks, in which nodes are characterized by hidden variables reflecting the properties of nodes and the occupied probability of each link is determined by the hidden variables of the end nodes, is studied in this paper. By the mean field theory, the analytical expressions for the phase of percolation transition is deduced. It is determined by the distribution of the hidden variables for the nodes and the occupied probability between pairs of them. Moreover, the analytical expressions obtained are checked by means of numerical simulations on a particular model. Besides, the general model can be applied to describe and control practical diffusion models, such as disease diffusion model, scientists cooperation networks, and so on.

Keywords: complex networks, percolation transition, hidden variable, occupied probability.

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Authors: Zhichao Jiao, Craig Farnham, Jihui Yuan, Kazuo Emura

Abstract:

It is common to use the outdoor design weather data to select the air-conditioning capacity in the building design stage. The meteorological elements of outdoor design weather data are usually selected based on their excess frequency separately while the dependency between the elements is not well considered. It means that the simultaneous occurrence probability of these elements is smaller than the original excess frequency which may cause an overestimation of selecting air-conditioning capacity. Therefore, the copula approach which can capture the dependency between multivariate data was used to model the joint distributions of the meteorological elements, like air temperature and global solar radiation. We suggest a method based on the specific simultaneous occurrence probability of these two elements of selecting more credible outdoor design conditions. The hourly weather data at 12 noon from 2001 to 2010 in Tokyo, Japan are used to analyze the dependency structure and joint distribution, the Gaussian copula represents the dependence of data best. According to calculating the air temperature and global solar radiation in specific simultaneous occurrence probability and the common exceeding, the results show that both the air temperature and global solar radiation based on simultaneous occurrence probability are lower than these based on the conventional method in the same probability.

Keywords: Copula approach, Design weather database, energy conservation, HVAC.

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Authors: M. Ranjeeth, S. Anuradha

Abstract:

Spectrum sensing is the main feature of cognitive radio technology. Spectrum sensing gives an idea of detecting the presence of the primary users in a licensed spectrum. In this paper we compare the theoretical results of detection probability of different fading environments like Rayleigh, Rician, Nakagami-m fading channels with the simulation results using energy detection based spectrum sensing. The numerical results are plotted as Pf Vs Pd for different SNR values, fading parameters. It is observed that Nakagami fading channel performance is better than other fading channels by using energy detection in spectrum sensing. A MATLAB simulation test bench has been implemented to know the performance of energy detection in different fading channel environment.

Keywords: Spectrum sensing, Energy detection, fading channels, Probability of detection, probability of false alarm.

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Authors: A. Zanaz, S. Yotte, F. Fouchal, A. Chateauneuf

Abstract:

This paper presents a methodology for probabilistic assessment of bearing capacity and prediction of failure mechanism of masonry vaults at the ultimate state with consideration of the natural variability of Young’s modulus of stones. First, the computation model is explained. The failure mode corresponds to the four-hinge mechanism. Based on this consideration, the study of a vault composed of 16 segments is presented. The Young’s modulus of the segments is considered as random variable defined by a mean value and a coefficient of variation. A relationship linking the vault bearing capacity to the voussoirs modulus variation is proposed. The most probable failure mechanisms, in addition to that observed in the deterministic case, are identified for each variability level as well as their probability of occurrence. The results show that the mechanism observed in the deterministic case has decreasing probability of occurrence in terms of variability, while the number of other mechanisms and their probability of occurrence increases with the coefficient of variation of Young’s modulus. This means that if a significant change in the Young’s modulus of the segments is proven, taking it into account in computations becomes mandatory, both for determining the vault bearing capacity and for predicting its failure mechanism.

Keywords: Masonry, mechanism, probability, variability, vault.

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Authors: Alhusein Almahjoub, Dongyu Qiu

Abstract:

This paper deals with the random access procedure in next-generation networks and presents the solution to reduce total service time (TST) which is one of the most important performance metrics in current and future internet of things (IoT) based networks. The proposed solution focuses on the calculation of optimal transmission probability which maximizes the success probability and reduces TST. It uses the information of several idle preambles in every time slot, and based on it, it estimates the number of backlogged IoT devices using Naïve Bayes estimation which is a type of supervised learning in the machine learning domain. The estimation of backlogged devices is necessary since optimal transmission probability depends on it and the eNodeB does not have information about it. The simulations are carried out in MATLAB which verify that the proposed solution gives excellent performance.

Keywords: Random access, LTE/LTE-A, 5G, machine learning, Naïve Bayes estimation.

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Authors: D. De-León-Escobedo, D. J. Delgado-Hernández, S. Pérez

Abstract:

A probabilistic formulation to assess the slopes safety under the hazard of strong storms is presented and illustrated through a slope in Mexico. The formulation is based on the classical safety factor (SF) used in practice to appraise the slope stability, but it is introduced the treatment of uncertainties, and the slope failure probability is calculated as the probability that SF<1. As the main hazard is the rainfall on the area, statistics of rainfall intensity and duration are considered and modeled with an exponential distribution. The expected life-cycle cost is assessed by considering a monetary value on the slope failure consequences. Alternative mitigation measures are simulated, and the formulation is used to get the measures driving to the optimal one (minimum life-cycle costs). For the example, the optimal mitigation measure is the reduction on the slope inclination angle.

Keywords: Expected life-cycle cost, failure probability, slopes failure, storms.

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Authors: Po-Wen Chen, Jin-Yu Wu, Md. Manirul Ali, Yang Peng, Chen-Te Chang, Der-Jun Jan

Abstract:

Dynamics of cathode spot has become a major part of vacuum arc discharge with its high academic interest and wide application potential. In this article, using a three-dimensional statistical model, we simulate the distribution of the ignition probability of a new cathode spot occurring in different magnetic pressure on old cathode spot surface and at different arcing time. This model for the ignition probability of a new cathode spot was proposed in two typical situations, one by the pure isotropic random walk in the absence of an external magnetic field, other by the retrograde motion in external magnetic field, in parallel with the cathode surface. We mainly focus on developed relationship between the ignition probability density distribution of a new cathode spot and the external magnetic field.

Keywords: Cathode spot, vacuum arc discharge, transverse magnetic field, random walk.

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Authors: Pradip Deb

Abstract:

Quantitative radiobiological models can be used to assess the optimum clinical outcome from sophisticated therapeutic modalities by calculating tumor control probability (TCP) and normal tissue complication probability (NTCP). In this study two 3D-CRT and an IMRT treatment plans were developed with an initial prescription dose of 60 Gy in 2 Gy/fraction to prostate. Sensitivity of TCP and Complication free tumor control probability (P+) to the different values of α/β ratio was investigated for various prescription doses planned to be delivered in either a fixed number of fractions (I) or in a fixed dose per fraction (II) in each of the three different treatment plans. High dose/fraction and high α/β value result in comparatively smaller P+ and IMRT plans resulted in the highest P+, mainly due to the decrease in NTCP. If α/β is lower than expected, better tumor control can be achieved by increasing dose/fraction but decreasing the number of fractions.

Keywords: Linear Quadratic Model, TCP, NTCP, α/β ratio.

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Authors: M. Kargar, F. Gharbalchi

Abstract:

In this paper a new method is suggested for distributed data-mining by the probability patterns. These patterns use decision trees and decision graphs. The patterns are cared to be valid, novel, useful, and understandable. Considering a set of functions, the system reaches to a good pattern or better objectives. By using the suggested method we will be able to extract the useful information from massive and multi-relational data bases.

Keywords: Data-mining, Decision tree, Decision graph, Pattern, Relationship.

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Authors: A. Habibizad Navin, M. Naghian Fesharaki, M. Mirnia, M. Kargar

Abstract:

In this paper we introduce Digital Probability Hyper Digraph for modeling random variable as the hierarchical data-oriented model.

Keywords: Data-Oriented Models, Data Structure, DigitalProbability Hyper Digraph, Random Variable, Statistic andProbability.

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Authors: Lokesh Varshney, R. K. Saket

Abstract:

This paper presents reliability indices evaluation of the rotor core magnetization of the induction motor operated as a self excited induction generator by using probability distribution approach and Monte Carlo simulation. Parallel capacitors with calculated minimum capacitive value across the terminals of the induction motor operated as a SEIG with unregulated shaft speed have been connected during the experimental study. A three phase, 4 poles, 50Hz, 5.5 hp, 12.3A, 230V induction motor coupled with DC Shunt Motor was tested in the electrical machine laboratory with variable reactive loads. Based on this experimental study, it is possible to choose a reliable induction machines operated as a SEIG for unregulated renewable energy application in remote area or where grid is not available. Failure density function, cumulative failure distribution function, survivor function, hazard model, probability of success and probability of failure for reliability evaluation of the three phase induction motor operating as a SEIG have been presented graphically in this paper.

Keywords: Residual magnetism, magnetization curve, induction motor, self excited induction generator, probability distribution, Monte Carlo simulation.

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Authors: N. A. Salim, M. M. Othman, I. Musirin, M. S. Serwan

Abstract:

Hidden failure in a protection system has been recognized as one of the main reasons which may cause to a power system instability leading to a system cascading collapse. This paper presents a computationally systematic approach used to obtain the estimated average probability of a system cascading collapse by considering the effect of probability hidden failure in a protection system. The estimated average probability of a system cascading collapse is then used to determine the severe loading condition contributing to the higher risk of critical system cascading collapse. This information is essential to the system utility since it will assist the operator to determine the highest point of increased system loading condition prior to the event of critical system cascading collapse.

Keywords: Critical system cascading collapse, protection system hidden failure, severe loading condition.

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Authors: Andy Handouyahia, Tony Haddad, Frank Eaton

Abstract:

Recent quasi-experimental evaluation of the Canadian Active Labour Market Policies (ALMP) by Human Resources and Skills Development Canada (HRSDC) has provided an opportunity to examine alternative methods to estimating the incremental effects of Employment Benefits and Support Measures (EBSMs) on program participants. The focus of this paper is to assess the efficiency and robustness of inverse probability weighting (IPW) relative to kernel matching (KM) in the estimation of program effects. To accomplish this objective, the authors compare pairs of 1,080 estimates, along with their associated standard errors, to assess which type of estimate is generally more efficient and robust. In the interest of practicality, the authorsalso document the computationaltime it took to produce the IPW and KM estimates, respectively.

Keywords: Treatment effect, causal inference, observational studies, Propensity score based matching, Kernel Matching, Inverse Probability Weighting, Estimation methods for incremental effect.

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Authors: Kong Fah Tee, Lutfor Rahman Khan, Hongshuang Li

Abstract:

An advanced Monte Carlo simulation method, called Subset Simulation (SS) for the time-dependent reliability prediction for underground pipelines has been presented in this paper. The SS can provide better resolution for low failure probability level with efficient investigating of rare failure events which are commonly encountered in pipeline engineering applications. In SS method, random samples leading to progressive failure are generated efficiently and used for computing probabilistic performance by statistical variables. SS gains its efficiency as small probability event as a product of a sequence of intermediate events with larger conditional probabilities. The efficiency of SS has been demonstrated by numerical studies and attention in this work is devoted to scrutinise the robustness of the SS application in pipe reliability assessment. It is hoped that the development work can promote the use of SS tools for uncertainty propagation in the decision-making process of underground pipelines network reliability prediction.

Keywords: Underground pipelines, Probability of failure, Reliability and Subset Simulation.

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Authors: Fenglong Guo, Dingcheng Wang

Abstract:

This paper studies ruin probabilities in two discrete-time risk models with premiums, claims and rates of interest modelled by three autoregressive moving average processes. Generalized Lundberg inequalities for ruin probabilities are derived by using recursive technique. A numerical example is given to illustrate the applications of these probability inequalities.

Keywords: Lundberg inequality, NWUC, Renewal recursive technique, Ruin probability

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Authors: Viriyavudh Sim, Woo Young Jung

Abstract:

The failure of roof cladding mostly occurs due to the failing of the connection between claddings and purlins, which is the pull-out of the screw connecting the two parts when the pull-out load, i.e. typhoon, is higher than the resistance of the connection screw. As typhoon disasters in Korea are constantly on the rise, probability risk assessment (PRA) has become a vital tool to evaluate the performance of civil structures. In this study, we attempted to determine the fragility of roof cladding with the screw connection. Experimental study was performed to evaluate the pull-out resistance of screw joints between honeycomb panels and back frames. Subsequently, by means of Monte Carlo Simulation method, probability of failure for these types of roof cladding was determined. The results that the failure of roof cladding was depends on their location on the roof, for example, the edge most panel has the highest probability of failure.

Keywords: Monte Carlo Simulation, roof cladding, screw pull-out strength, wind fragility

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Authors: J. Daba, J. Dubois

Abstract:

In this work, we improve a previously developed segmentation scheme aimed at extracting edge information from speckled images using a maximum likelihood edge detector. The scheme was based on finding a threshold for the probability density function of a new kernel defined as the arithmetic mean-to-geometric mean ratio field over a circular neighborhood set and, in a general context, is founded on a likelihood random field model (LRFM). The segmentation algorithm was applied to discriminated speckle areas obtained using simple elliptic discriminant functions based on measures of the signal-to-noise ratio with fractional order moments. A rigorous stochastic analysis was used to derive an exact expression for the cumulative density function of the probability density function of the random field. Based on this, an accurate probability of error was derived and the performance of the scheme was analysed. The improved segmentation scheme performed well for both simulated and real images and showed superior results to those previously obtained using the original LRFM scheme and standard edge detection methods. In particular, the false alarm probability was markedly lower than that of the original LRFM method with oversegmentation artifacts virtually eliminated. The importance of this work lies in the development of a stochastic-based segmentation, allowing an accurate quantification of the probability of false detection. Non visual quantification and misclassification in medical ultrasound speckled images is relatively new and is of interest to clinicians.

Keywords: Discriminant function, false alarm, segmentation, signal-to-noise ratio, skewness, speckle.

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Authors: Seon Soon Choi

Abstract:

The principal purpose of this paper is to find the influence of maximum fatigue load on the probabilistic aspect of fatigue crack propagation life at a specified grown crack in magnesium alloys. The experiments of fatigue crack propagation are carried out in laboratory air under different conditions of the maximum fatigue loads to obtain the fatigue crack propagation data for the statistical analysis. In order to analyze the probabilistic aspect of fatigue crack propagation life, the goodness-of fit test for probability distribution of the fatigue crack propagation life at a specified grown crack is implemented through Anderson-Darling test. The good probability distribution of the fatigue crack propagation life is also verified under the conditions of the maximum fatigue loads.

Keywords: Fatigue crack propagation life, magnesium alloys, maximum fatigue load, probability.

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Authors: Jan Rychtar, Brian Stadler

Abstract:

We study how the outcome of evolutionary dynamics on graphs depends on a randomness on the graph structure. We gradually change the underlying graph from completely regular (e.g. a square lattice) to completely random. We find that the fixation probability increases as the randomness increases; nevertheless, the increase is not significant and thus the fixation probability could be estimated by the known formulas for underlying regular graphs.

Keywords: evolutionary dynamics, small-world networks

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Authors: Anant Oonsivilai, Kenedy A. Greyson

Abstract:

The demand of the energy management systems (EMS) set forth by modern power systems requires fast energy management systems. Contingency analysis is among the functions in EMS which is time consuming. In order to handle this limitation, this paper introduces agent based technology in the contingency analysis. The main function of agents is to speed up the performance. Negotiations process in decision making is explained and the issue set forth is the minimization of the operating costs. The IEEE 14 bus system and its line outage have been used in the research and simulation results are presented.

Keywords: Agents, model, negotiation, optimal dispatch, powersystems.

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Authors: M. A. Tayfun, M. A. Alkhalidi

Abstract:

The exact theoretical expression describing the probability distribution of nonlinear sea-surface elevations derived from the second-order narrowband model has a cumbersome form that requires numerical computations, not well-disposed to theoretical or practical applications. Here, the same narrowband model is reexamined to develop a simpler closed-form approximation suitable for theoretical and practical applications. The salient features of the approximate form are explored, and its relative validity is verified with comparisons to other readily available approximations, and oceanic data.

Keywords: Ocean waves, probability distributions, second-order nonlinearities, skewness coefficient, wave steepness.

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Authors: N.R.N. Idris

Abstract:

This study uses simulated meta-analysis to assess the effects of publication bias on meta-analysis estimates and to evaluate the efficacy of the trim and fill method in adjusting for these biases. The estimated effect sizes and the standard error were evaluated in terms of the statistical bias and the coverage probability. The results demonstrate that if publication bias is not adjusted it could lead to up to 40% bias in the treatment effect estimates. Utilization of the trim and fill method could reduce the bias in the overall estimate by more than half. The method is optimum in presence of moderate underlying bias but has minimal effects in presence of low and severe publication bias. Additionally, the trim and fill method improves the coverage probability by more than half when subjected to the same level of publication bias as those of the unadjusted data. The method however tends to produce false positive results and will incorrectly adjust the data for publication bias up to 45 % of the time. Nonetheless, the bias introduced into the estimates due to this adjustment is minimal

Keywords: Publication bias, Trim and Fill method, percentage relative bias, coverage probability

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Authors: M. I. Youssef, A. E. Emam, M. Abd Elghany

Abstract:

In this paper, a residue number arithmetic is used in direct sequence spread spectrum system, this system is evaluated and the bit error probability of this system is compared to that of non residue number system. The effect of channel bandwidth, PN sequences, multipath effect and modulation scheme are studied. A Matlab program is developed to measure the signal-to-noise ratio (SNR), and the bit error probability for the various schemes.

Keywords: Spread Spectrum, Direct sequence, Bit errorprobability and Residue number system.

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Authors: Ahmad Habibizad Navin, Mehdi Naghian Fesharaki, Mirkamal Mirnia, Mohamad Teshnelab, Ehsan Shahamatnia

Abstract:

In this paper we introduce new data oriented modeling of uniform random variable well-matched with computing systems. Due to this conformity with current computers structure, this modeling will be efficiently used in statistical inference.

Keywords: Uniform random variable, Data oriented modeling, Statistical inference, Prodigraph, Statistically complete tree, Uniformdigital probability digraph, Uniform n-complete probability tree.

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Authors: Pooja, Megha Kulshrestha, V. K. Banga, Parvinder S. Sandhu

Abstract:

To support mobility in ATM networks, a number of technical challenges need to be resolved. The impact of handoff schemes in terms of service disruption, handoff latency, cost implications and excess resources required during handoffs needs to be addressed. In this paper, a one phase handoff and route optimization solution using reserved PVCs between adjacent ATM switches to reroute connections during inter-switch handoff is studied. In the second phase, a distributed optimization process is initiated to optimally reroute handoff connections. The main objective is to find the optimal operating point at which to perform optimization subject to cost constraint with the purpose of reducing blocking probability of inter-switch handoff calls for delay tolerant traffic. We examine the relation between the required bandwidth resources and optimization rate. Also we calculate and study the handoff blocking probability due to lack of bandwidth for resources reserved to facilitate the rapid rerouting.

Keywords: Wireless ATM, Mobility, Latency, Optimization rateand Blocking Probability.

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Authors: Zviad Ghadua, Biswa Bhattacharya

Abstract:

The Flash Flood Guidance (FFG) provides the rainfall amount of a given duration necessary to cause flooding. The approach is based on the development of rainfall-runoff curves, which helps us to find out the rainfall amount that would cause flooding. An alternative approach, mostly experimented with Italian Alpine catchments, is based on determining threshold discharges from past events and on finding whether or not an oncoming flood has its magnitude more than some critical discharge thresholds found beforehand. Both approaches suffer from large uncertainties in forecasting flash floods as, due to the simplistic approach followed, the same rainfall amount may or may not cause flooding. This uncertainty leads to the question whether a probabilistic model is preferable over a deterministic one in forecasting flash floods. We propose the use of a Bayesian probabilistic approach in flash flood forecasting. A prior probability of flooding is derived based on historical data. Additional information, such as antecedent moisture condition (AMC) and rainfall amount over any rainfall thresholds are used in computing the likelihood of observing these conditions given a flash flood has occurred. Finally, the posterior probability of flooding is computed using the prior probability and the likelihood. The variation of the computed posterior probability with rainfall amount and AMC presents the suitability of the approach in decision making in an uncertain environment. The methodology has been applied to the Posina basin in Italy. From the promising results obtained, we can conclude that the Bayesian approach in flash flood forecasting provides more realistic forecasting over the FFG.

Keywords: Flash flood, Bayesian, flash flood guidance, FFG, forecasting, Posina.

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Authors: Abdulkadir Abu Lawal

Abstract:

The study was carried out to establish the probability density function of some selected building construction projects of similar complexity delivered using Bill of Quantities (BQ) and Lump Sum (LS) forms of contract, and to draw a reliability scenario for each form of contract. 30 of such delivered projects are analyzed for each of the contract forms using Weibull Analysis, and their Weibull functions (α, and β) are determined based on their completion times. For the BQ form of contract delivered projects, α is calculated as 1.6737E20 and β as + 0.0115 and for the LS form, α is found to be 5.6556E03 and β is determined as + 0.4535. Using these values, respective probability density functions are calculated and plotted, as handy tool for risk analysis of future projects of similar characteristics. By input of variables from other projects, decision making processes can be made for a whole project or its components using EVM Analysis in project evaluation and review techniques. This framework, as a quantitative approach, depends on the assumption of normality in projects completion time, it can help greatly in determining the completion time probability for veritable projects using any of the contract forms under consideration. Projects aspects that are not amenable to measurement, on the other hand, can be analyzed using fuzzy sets and fuzzy logic. This scenario can be drawn for different types of building construction projects, and using different suitable forms of contract in projects delivery.

Keywords: Building construction, Projects, Forms of contract, Probability density function, Reliability scenario.

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Authors: Badarch Tuyatsetseg

Abstract:

This paper presents parametric probability density models for call holding times (CHTs) into emergency call center based on the actual data collected for over a week in the public Emergency Information Network (EIN) in Mongolia. When the set of chosen candidates of Gamma distribution family is fitted to the call holding time data, it is observed that the whole area in the CHT empirical histogram is underestimated due to spikes of higher probability and long tails of lower probability in the histogram. Therefore, we provide the Gaussian parametric model of a mixture of lognormal distributions with explicit analytical expressions for the modeling of CHTs of PSNs. Finally, we show that the CHTs for PSNs are fitted reasonably by a mixture of lognormal distributions via the simulation of expectation maximization algorithm. This result is significant as it expresses a useful mathematical tool in an explicit manner of a mixture of lognormal distributions.

Keywords: A mixture of lognormal distributions, modeling call holding times, public safety network.

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Authors: Petr Gurný

Abstract:

One of the most important tasks in the risk management is the correct determination of probability of default (PD) of particular financial subjects. In this paper a possibility of determination of financial institution’s PD according to the creditscoring models is discussed. The paper is divided into the two parts. The first part is devoted to the estimation of the three different models (based on the linear discriminant analysis, logit regression and probit regression) from the sample of almost three hundred US commercial banks. Afterwards these models are compared and verified on the control sample with the view to choose the best one. The second part of the paper is aimed at the application of the chosen model on the portfolio of three key Czech banks to estimate their present financial stability. However, it is not less important to be able to estimate the evolution of PD in the future. For this reason, the second task in this paper is to estimate the probability distribution of the future PD for the Czech banks. So, there are sampled randomly the values of particular indicators and estimated the PDs’ distribution, while it’s assumed that the indicators are distributed according to the multidimensional subordinated Lévy model (Variance Gamma model and Normal Inverse Gaussian model, particularly). Although the obtained results show that all banks are relatively healthy, there is still high chance that “a financial crisis” will occur, at least in terms of probability. This is indicated by estimation of the various quantiles in the estimated distributions. Finally, it should be noted that the applicability of the estimated model (with respect to the used data) is limited to the recessionary phase of the financial market.

Keywords: Credit-scoring Models, Multidimensional Subordinated Lévy Model, Probability of Default.

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Authors: S. Dan'azumi, S. Shamsudin, A. A. Rahman

Abstract:

Rainfall data at fine resolution and knowledge of its characteristics plays a major role in the efficient design and operation of agricultural, telecommunication, runoff and erosion control as well as water quality control systems. The paper is aimed to study the statistical distribution of hourly rainfall depth for 12 representative stations spread across Peninsular Malaysia. Hourly rainfall data of 10 to 22 years period were collected and its statistical characteristics were estimated. Three probability distributions namely, Generalized Pareto, Exponential and Gamma distributions were proposed to model the hourly rainfall depth, and three goodness-of-fit tests, namely, Kolmogorov-Sminov, Anderson-Darling and Chi-Squared tests were used to evaluate their fitness. Result indicates that the east cost of the Peninsular receives higher depth of rainfall as compared to west coast. However, the rainfall frequency is found to be irregular. Also result from the goodness-of-fit tests show that all the three models fit the rainfall data at 1% level of significance. However, Generalized Pareto fits better than Exponential and Gamma distributions and is therefore recommended as the best fit.

Keywords: Goodness-of-fit test, Hourly rainfall, Malaysia, Probability distribution.

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