Goodness-of-Fit Tests for Uniformity of Probability Distribution Law

AbstractThis study was designed to find the best-fit probability distribution of annual maximum rainfall based on a twenty-four-hour sample in the northern regions of Pakistan using four probability distributions: normal, log-normal, log-Pearson type-III and Gumbel max. Based on the scores of goodness of fit tests, the normal distribution was found to be the best-fit probability distribution at the Mardan rainfall gauging station. The log-Pearson type-III distribution was found to be the best-fit probability distribution at the rest of the rainfall gauging stations. The maximum values of expected rainfall were calculated using the best-fit probability distributions and can be used by design engineers in future research.

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Estimating the Best-Fitted Probability Distribution for Monthly Maximum Temperature at the Sylhet Station in Bangladesh

Journal of Mathematics and Statistics Studies ◽

10.32996/jmss.2021.2.2.7 ◽

2021 ◽

Vol 2 (2) ◽

pp. 60-67

Author(s):

Rashidul Hasan Rashidul Hasan

Keyword(s):

Probability Distribution ◽

Goodness Of Fit ◽

Probability Distributions ◽

Probability Model ◽

Temperature Data ◽

Maximum Temperature ◽

Chi Square ◽

Goodness Of Fit Tests ◽

Anderson Darling ◽

Log Normal

The estimation of a suitable probability model depends mainly on the features of available temperature data at a particular place. As a result, existing probability distributions must be evaluated to establish an appropriate probability model that can deliver precise temperature estimation. The study intended to estimate the best-fitted probability model for the monthly maximum temperature at the Sylhet station in Bangladesh from January 2002 to December 2012 using several statistical analyses. Ten continuous probability distributions such as Exponential, Gamma, Log-Gamma, Beta, Normal, Log-Normal, Erlang, Power Function, Rayleigh, and Weibull distributions were fitted for these tasks using the maximum likelihood technique. To determine the model’s fit to the temperature data, several goodness-of-fit tests were applied, including the Kolmogorov-Smirnov test, Anderson-Darling test, and Chi-square test. The Beta distribution is found to be the best-fitted probability distribution based on the largest overall score derived from three specified goodness-of-fit tests for the monthly maximum temperature data at the Sylhet station.

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Temporal and spatial variations in annual rainfall distribution in Erbil province

Outlook on Agriculture ◽

10.1177/0030727018762968 ◽

2018 ◽

Vol 47 (1) ◽

pp. 59-67

Author(s):

Tariq H Karim ◽

Dawod R Keya ◽

Zahir A Amin

Keyword(s):

Probability Distribution ◽

Goodness Of Fit ◽

Kendall Test ◽

Distribution Functions ◽

Annual Rainfall ◽

Maximum Rainfall ◽

Probability Distribution Functions ◽

Goodness Of Fit Tests ◽

Annual Maximum Rainfall ◽

Best Fit

This study aimed to determine the best fit probability distribution of annual maximum rainfall using data from nine stations within Erbil province using different statistical analyses. Nine commonly used probability distribution functions, namely Normal, Lognormal (LN), one-parameter gamma (1P-G), 2P-G, 3P-G, Log Pearson, Weibull, Pareto, and Beta, were assessed. On the basis of maximum overall score, obtained by adding individual point scores from three selected goodness-of-fit tests, the best fit probability distribution was identified. Results showed that the 2P-G distribution and LN distribution were the best fit probability distribution functions for annual rainfall for the region. The analysis of annual rainfall records in Erbil city spanning from 1964 to 2013, covering three periods, also revealed significant temporal changes in the shape and scale parameter patterns of the fitted gamma distribution. Based on the reliable annual rainfall data in the region, the shape and scale parameters were then regionalized, hence it is possible to find the parameter values for any desired location within the study area. The Mann–Kendall test results indicated that there was a decreasing trend in rainfall over most of the study area in recent decades.

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Best Fitted Distribution For Meteorological Data In Kuala Krai

Journal of Statistical Modelling and Analytics ◽

10.22452/josma.vol3no1.2 ◽

2021 ◽

Vol 3 (1) ◽

pp. 16-25

Author(s):

Siti Mariam Norrulashikin ◽

Fadhilah Yusof ◽

Siti Rohani Mohd Nor ◽

Nur Arina Bazilah Kamisan

Keyword(s):

Climate Change ◽

Probability Distribution ◽

Goodness Of Fit ◽

Probability Distributions ◽

Meteorological Data ◽

Cumulative Distribution ◽

Distribution Model ◽

Data Series ◽

Distribution Models ◽

Goodness Of Fit Tests

Modeling meteorological variables is a vital aspect of climate change studies. Awareness of the frequency and magnitude of climate change is a critical concern for mitigating the risks associated with climate change. Probability distribution models are valuable tools for a frequency study of climate variables since it measures how the probability distribution able to fit well in the data series. Monthly meteorological data including average temperature, wind speed, and rainfall were analyzed in order to determine the most suited probability distribution model for Kuala Krai district. The probability distributions that were used in the analysis were Beta, Burr, Gamma, Lognormal, and Weibull distributions. To estimate the parameters for each distribution, the maximum likelihood estimate (MLE) was employed. Goodness-of-fit tests such as the Kolmogorov-Smirnov, and Anderson-Darling tests were conducted to assess the best suited model, and the test's reliability. Results from statistical studies indicate that Burr distributions better characterize the meteorological data of our research. The graph of probability density function, cumulative distribution function as well as Q-Q plot are presented.

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Selecting the best probability distribution for at-site flood frequency analysis; a study of Torne River

SN Applied Sciences ◽

10.1007/s42452-019-1584-z ◽

2019 ◽

Vol 1 (12) ◽

Cited By ~ 2

Author(s):

Mahmood Ul Hassan ◽

Omar Hayat ◽

Zahra Noreen

Keyword(s):

Probability Distribution ◽

Frequency Analysis ◽

Goodness Of Fit ◽

Direct Method ◽

Estimation Method ◽

Likelihood Estimation ◽

Flood Frequency ◽

Flood Frequency Analysis ◽

Goodness Of Fit Tests ◽

Pearson Type

AbstractAt-site flood frequency analysis is a direct method of estimation of flood frequency at a particular site. The appropriate selection of probability distribution and a parameter estimation method are important for at-site flood frequency analysis. Generalized extreme value, three-parameter log-normal, generalized logistic, Pearson type-III and Gumbel distributions have been considered to describe the annual maximum steam flow at five gauging sites of Torne River in Sweden. To estimate the parameters of distributions, maximum likelihood estimation and L-moments methods are used. The performance of these distributions is assessed based on goodness-of-fit tests and accuracy measures. At most sites, the best-fitted distributions are with LM estimation method. Finally, the most suitable distribution at each site is used to predict the maximum flood magnitude for different return periods.

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AN ALTERNATIVE TEST FOR UNIFORMITY

International Journal of Reliability Quality and Safety Engineering ◽

10.1142/s0218539309003435 ◽

2009 ◽

Vol 16 (04) ◽

pp. 343-356 ◽

Cited By ~ 5

Author(s):

ZHENMIN CHEN ◽

CHUNMIAO YE

Keyword(s):

Probability Distribution ◽

Goodness Of Fit ◽

Integral Transformation ◽

Test Statistic ◽

Goodness Of Fit Test ◽

Underlying Distribution ◽

Goodness Of Fit Tests ◽

Kolmogorov Smirnov ◽

Alternative Test ◽

Smirnov Test

Improving power of goodness-of-fit tests is an important research topic in statistics. The goal of the goodness-of-fit test is to check whether the underlying probability distribution, from which a sample is drawn, differs from a hypothesized distribution. Numerous research papers have been published in this area. It has been shown that the power of the existing goodness-of-fit tests in the literature is unsatisfactory when the alternative distributions are of V-shape or when the sample sizes are small. This motivates the development of more powerful test statistics. In this research, a new test statistic is proposed. The result can be used to test whether the underlying probability distribution differs from a uniform distribution. By applying the probability integral transformation, the proposed test statistic can be used to check whether the underlying distribution differs from any hypothesized distribution. The performance of the method proposed in this research is compared with the Kolmogorov–Smirnov test, which is a widely adopted statistical test in the literature. It has been shown that the test proposed in this proposal is more powerful than the Kolmogorov–Smirnov test in some cases.

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