Goodness of fit test for the generalized Rayleigh distribution with unknown parameters

Abd-Elfattah, A. M.

doi:10.1080/00949650903348155

Cited by 32 publications

(32 citation statements)

References 23 publications

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“…The expressions and their applying steps of these statistics can be found in Abd‐Elfattah et al . () as well as Song and Singh (). The computed sample values of D n ,

W_{n}^{2}

A_{n}^{2}

and

U_{n}^{2}

for drought severity and peak are given in Tables and , respectively.…”

Section: Methodsmentioning

confidence: 87%

Multivariate drought characteristics using trivariate Gaussian and Student t copulas

Song

Ren

et al. 2012

Hydrological Processes

125

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This study aims to investigate the changing properties of drought events in Weihe River basin, China, by modeling the multivariate joint distribution of drought duration, severity and peak using trivariate Gaussian and Student t copulas. Monthly precipitations of Xi'an gauge are used to illustrate the meta-elliptical copula-based methodology for a single-station application. Gaussian and Student t copulas are found to produce a better fit comparing with other six symmetrical and asymmetrical Archimedean copulas, and, checked by the goodness-of-fit tests based on a modified bootstrap version of Rosenblatt's transformation, both of them are acceptable to model the multivariate joint distribution of drought variables. Gaussian copula, the best fitting, is employed to construct the dependence structures of positively associated drought variables so as to obtain the multivariate joint and conditional probabilities of droughts. A Kendall's return period (KRP) introduced by Salvadori and De Michele (2010) is then adopted to assess the multivariate recurrent properties of drought events, and its spatial distributions indicate that prolonged droughts are likely to break out with rather short recurrence intervals in the whole region, while drought status in the southeast seems to be severer than the northwest. The study is of some merits in terms of multivariate drought modeling using a preferable copula-based method, the results of which could serve as a reference for regional drought defense and water resources management.

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“…The expressions and their applying steps of these statistics can be found in Abd‐Elfattah et al . () as well as Song and Singh (). The computed sample values of D n ,

W_{n}^{2}

A_{n}^{2}

and

U_{n}^{2}

for drought severity and peak are given in Tables and , respectively.…”

Section: Methodsmentioning

confidence: 87%

Multivariate drought characteristics using trivariate Gaussian and Student t copulas

Song

Ren

et al. 2012

Hydrological Processes

125

View full text Add to dashboard Cite

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“…Abd-Elfattah and Omima [31] addressed the estimation of the unknown parameters of the generalized Fréchet distribution. Abd-Elfattah et al [32] introduced the goodness of fit tests for generalized Fréchet distribution. Al-Nassar and Al-Omari [33] studied the acceptance sampling plan based on truncated life tests for exponentiated Fréchet distribution.…”

Section: The Exponentiated Fréchet Distribution (Efd)mentioning

confidence: 99%

Double-Acceptance Sampling Plan for Exponentiated Fréchet Distribution with Known Shape Parameters

Babu

Rao

Rosaiah

2021

Mathematical Problems in Engineering

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We suppose that a product’s lifetime follow the exponentiated Fréchet distribution of defined shape parameters. Based on this assumption, a double-acceptance sampling plan is constructed. The zero and one failure framework is essentially thought of: if no errors are found from the first sample, then the lot is approved; also, if at least two failures occur, it is rejected. In the first sample, if one failure is observed, then the second sample is taken and decided for the same length as the first one. The cumulative sample sizes of the first and second samples are determined on the basis of the stated confidence level of the consumer to ensure that the actual median is longer than the given life. As indicated by the various ratios of the actual median life to specified median lifetime, the operating characteristics are calculated and placed in presented tables. To decrease the risk of the producer at the predefined level, the minimum ratios of this sort are additionally obtained. Lastly, examples are provided for representation reasons for the proposed model.

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“…The exponential distribution was discussed by Balakrishnan and Basu (1995). Also, Hassan (2005) studied GOF for the generalized exponential distribution, Abd-Elfattah (2011) studied the generalized Rayleigh distribution, Wang (2008) discussed the GOF test for the exponential distribution based on progressively Type II censored sample, Allam and Zamanzade (2011) studied the case for generalized exponential distribution, Szynal and Wolynski (2012). Al-Omari and Zamanzade (2016) discussed the different goodness of fit tests for Rayleigh distribution in ranked set sampling.…”

Section: Introductionmentioning

confidence: 99%

Goodness-of-fit tests for the Compound Rayleigh distribution with application to real data

Badr

2019

Heliyon

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An important problem in statistics is to obtain information about the form of the population from which the sample is drawn. Goodness of fit (GOF) tests is employed to determine how well the observed sample data “fits” some proposed model. The well known standard goodness of fit tests; Kolomogorov-Smirnov (KS), Cramer von Mises (CVM) and Anderson-(AD) tests are used for continuous distributions. When the parameters are unknown, the standard tables for these tests are not valid. The complete sample procedures of goodness of fit tests are inappropriate for use with censored samples. The critical values obtained from published tables of the complete sample test statistic are necessarily conservative. In this paper, we obtain the tables of critical values of modified Kolmogorov-Smirnov (KS) test, Cramer-Von Mises (CVM) test and Anderson-Darling (AD) test for the Compound Rayleigh (CR) distribution with unknown parameters in the case of complete and type II censored samples. Furthermore, we present power comparison between KS test, CVM test and AD test for a number of alternative distributions. Applications of the considered distribution to real medical data sets given by Stablein et al. (1981) are presented.

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Goodness of fit test for the generalized Rayleigh distribution with unknown parameters

Cited by 32 publications

References 23 publications

Multivariate drought characteristics using trivariate Gaussian and Student t copulas

Multivariate drought characteristics using trivariate Gaussian and Student t copulas

Double-Acceptance Sampling Plan for Exponentiated Fréchet Distribution with Known Shape Parameters

Goodness-of-fit tests for the Compound Rayleigh distribution with application to real data

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