scholarly journals A New Goodness-of-Fit Test for the Two-Parameter Gamma Distribution

2022 ◽  
Vol 3 (1) ◽  
pp. 01-06
Author(s):  
Mbanefo S. Madukaife
Keyword(s):  
Gamma Distribution ◽  
Goodness Of Fit ◽  
Critical Values ◽  
Parameter Distribution ◽  
Goodness Of Fit Test ◽  
Gamma Distributions ◽  
Two Parameter

This paper proposes a new goodness-of-fit for the two-parameter distribution. It is based on a function of squared distances between empirical and theoretical quantiles of a set of observations being hypothesized to have come from the gamma distribution. The critical values of the proposed statistic are evaluated through extensive simulations of the unit-scaled gamma distributions and computations. The empirical powers of the statistic are obtained and compared with some well-known tests for the gamma distribution, and the results show that the proposed statistic can be recommended as a test for the gamma distribution.

scholarly journals A comparison of three parameter estimation methods of the gamma distribution of annual maximum low flow duration and deficit in the Upper Vistula catchment (Poland)

2018 ◽  
Vol 23 ◽  
pp. 00001
Author(s):  
Katarzyna Baran-Gurgul
Keyword(s):  
Gamma Distribution ◽  
Goodness Of Fit ◽  
Probability Distributions ◽  
Low Flow ◽  
Estimation Methods ◽  
Goodness Of Fit Test ◽  
Flow Duration ◽  
Distribution Parameters ◽  
Anderson Darling ◽  
Parameter Estimation Methods

Based on 30-year 24-hour flow sequences at 69 water gauging stations in the Upper Vistula catchment, it was determined that the probability distributions of the low flow duration and its maximum annual deficit can be described by the gamma distribution with the estimated parameters by the methods: MOM, the method of moments, LMOM, the method of linear moments, and MLE, the method of maximum likelihood. The stationarity of the time series was tested by the Mann-Kendall correlation using the Hamed and Rao variance correction. The low flows were defined by the SPA method, with the limit flow Q70%. The quality of the match was tested by the Anderson-Darling goodness of fit test. This test allowed accepting the gamma distribution in all analysed cases, regardless of the method used to estimate the distribution parameters, since the pv (p-values) values were greater than 5% (over 18% for Tmax and 7.5% for Vmax). The highest pv values for individual water gauging stations, as well as the highest 90% Tmax and Vmax quantiles were noted using LMOM to estimate the gamma distribution parameters. The highest 90% Tmax and Vmax quantiles were observed in the uppermost part of the studied area.

scholarly journals Modelling the COVID-19 Mortality Rate with a New Versatile Modification of the Log-Logistic Distribution

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Abdisalam Hassan Muse ◽  
Ahlam H. Tolba ◽  
Eman Fayad ◽  
Ola A. Abu Ali ◽  
M. Nagy ◽  
...  
Keyword(s):  
Mortality Rate ◽  
Goodness Of Fit ◽  
Likelihood Estimation ◽  
Cumulative Distribution ◽  
Logistic Distribution ◽  
Parameter Distribution ◽  
Unknown Parameters ◽  
Failure Rate Function ◽  
Competing Models ◽  
Two Parameter

The goal of this paper is to develop an optimal statistical model to analyze COVID-19 data in order to model and analyze the COVID-19 mortality rates in Somalia. Combining the log-logistic distribution and the tangent function yields the flexible extension log-logistic tangent (LLT) distribution, a new two-parameter distribution. This new distribution has a number of excellent statistical and mathematical properties, including a simple failure rate function, reliability function, and cumulative distribution function. Maximum likelihood estimation (MLE) is used to estimate the unknown parameters of the proposed distribution. A numerical and visual result of the Monte Carlo simulation is obtained to evaluate the use of the MLE method. In addition, the LLT model is compared to the well-known two-parameter, three-parameter, and four-parameter competitors. Gompertz, log-logistic, kappa, exponentiated log-logistic, Marshall–Olkin log-logistic, Kumaraswamy log-logistic, and beta log-logistic are among the competing models. Different goodness-of-fit measures are used to determine whether the LLT distribution is more useful than the competing models in COVID-19 data of mortality rate analysis.

Comparison of stochastic models of rainfall processes in mountainous climatic conditions

2010 ◽  
Vol 1 (2) ◽  
pp. 135-146
Author(s):  
J. Y. Lee ◽  
M. Y. Han ◽  
D. K. Kim ◽  
W. H. Ji
Keyword(s):  
Exponential Distribution ◽  
Gamma Distribution ◽  
Rainwater Harvesting ◽  
Daily Rainfall ◽  
Percentage Error ◽  
Parameter Distribution ◽  
Mountainous Region ◽  
Simpler Algorithm ◽  
Two Parameter ◽  
Mixed Exponential Distribution

The main objective of this work was to find a stochastic simulation model that was suitable for designing a rainwater harvesting system for agricultural water utilization and irrigation water in a mountainous region. Several models were applied using daily rainfall data from two sites (Gangneung and Daekwanreung) to assess the accuracy and suitability of the model for simulating the daily rainfall. The amount of rainfall for the mountainous region was well described by a two-parameter gamma distribution and performed better than other distributions. However, validation tests revealed that the annual mean absolute percentage error (MAPE) was more than 10% at both locations. This result was different from some previous research in which a three-parameter mixed-exponential distribution was well described. In addition, although the exponential distribution was also well described by a second-order expression, the use of a one-parameter distribution had a simpler algorithm than the two-parameter gamma distribution and the three-parameter mixed-exponential distribution.

scholarly journals Probability Distribution of Rainfall in Medan

2019 ◽  
Vol 1 (2) ◽  
pp. 43-49 ◽  
Author(s):  
Elly Rosmaini
Keyword(s):  
Probability Distribution ◽  
Gamma Distribution ◽  
Goodness Of Fit ◽  
Monthly Rainfall ◽  
Rainfall Data ◽  
Goodness Of Fit Test ◽  
Normal Distributions ◽  
Lognormal Distributions ◽  
Kolmogorov Smirnov ◽  
Anderson Darling

In this paper we chose three stations in Medan City , Indonesia to estimate Monthly Rainfall Data i.e. Tuntungan, Tanjung Selamat, and Medan Selayang Stations. We took the data from 2007 to 2016. In this case fitted with Normal, Gamma, and Lognormal Distributions. To estimate parameters, we used this method. Furthermore, Kolmogorov-Smirnov and Anderson Darling tests were used the goodness-of-fit test. The Gamma and Normal Distributions is suitable for Tuntungan and Medan Selayang Stations were stated by Kolmogorov-Smirnov's test. Anderson Darling's test stated that Gamma Distribution was suitable for all stations.

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