Comparing estimation methods for the three-parameter kappa distribution with application to precipitation data

Sharafi, Maryam; Rezaei, Amir; Tavangar, Farideh

doi:10.1080/02626667.2021.1903010

Cited by 2 publications

(2 citation statements)

References 34 publications

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“…El-Morshedy et al (2020) gave bivariate exponentiated discrete Weibull distribution, Alotaibi et al (2020) introduced bivariate exponentiated half logistic distribution, El-Damcese et al (2015) derived bivariate exponentiated generalized Weibull-Gompertz distribution. For more literature on univariate and bivariate probabilistic models, see Pathak et al (2021), Pathak and Vellaisamy (2020), Azad (2021), Nazeri Tahroudi et al (2021), Azad (2022), andSharafi et al (2021).…”

Section: Introductionmentioning

confidence: 99%

On bivariate modelling using a new statistical distribution with homogeneous marginals

Poonia

Azad

2022

Intl Journal of Climatology

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Recent studies have shown that the univariate exponentiated Teissier distribution is an effective model for analysing rainfall data. A bivariate probability distribution offers greater insight into a process like a flood or drought than a univariate method for analysing the characteristics of environmental occurrences. As a result, in this study we developed a bivariate exponentiated Teissier distribution. The marginals of the proposed distribution model follow the exponentiated Teissier distribution. The cumulative distribution function of this bivariate model consists of continuous and singular components. The proposed model is shown to have several fundamental statistical properties, including joint cumulative distribution, joint density, marginals, and conditional distributions. Additionally, some copula functions are examined. The proposed model's parameter estimations are derived using the maximum likelihood method. Furthermore, the asymptotic confidence intervals are given for these estimates. A Monte Carlo simulation study with various sample sizes was performed to evaluate the behaviour of maximum likelihood estimates. Finally, we used football and flood datasets to demonstrate how the proposed model may be employed.

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Section: Introductionmentioning

confidence: 99%

On bivariate modelling using a new statistical distribution with homogeneous marginals

Poonia

Azad

2022

Intl Journal of Climatology

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“…The approximation of how often a certain event will take place is called frequency analysis (Hosking and Wallis, 1997). There are many statistical methods used in frequency analysis and estimation of the parameters of statistical distribution to predict the probability of upcoming events based on installation the previous observations on selected statistical distributions (Harun et al, 2017;Makhtar et al, 2016;Zhou et al, 2017;Sharafi et al, 2021;Murshed et al 2018). Some methods that rely on moments that have been used over a long period in frequency analysis are not always satisfactory especially when the sample is small.…”

Section: Introductionmentioning

confidence: 99%

Parameter estimate for three-parameter kappa distribution using LHmoments approach

al.¹

2022

Int. j. adv. appl. sci.

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The method of higher-order L-moments (LH-moment) was proposed as a more robust alternative compared to classical L-moments to characterize extreme events. The new derivation will be done for Mielke-Johnson’s Kappa and Three-Parameters Kappa Type-II (K3D-II) distributions based on the LH-moments approach. The data of maximum monthly rainfall for Embong station in Terengganu were used as a case study. The analyses were conducted using the classical L-moments method with η=0 and LH-moments methods with η=1, η=2, η=3 and η=4 for a complete data series and upper parts of the distributions. The most suitable distributions were determined based on the Mean Absolute Deviation Index (MADI), Mean Square Deviation Index (MSDI), and Correlation (r). Also, L-moment and LH-moment ratio diagrams were used to represent visual proofs of the results. The analysis showed that LH-moments methods at a higher order of K3D-II distribution best fit the data of maximum monthly rainfalls for the Embong station for the upper parts of the distribution compared to L-moments. The results also proved that whenever η increases, LH-moments reflect more and more characteristics of the upper part of the distribution. This seems to suggest that LH-moments estimates for the upper part of the distribution events are superior to L-moments in fitting the data of maximum monthly rainfalls.

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Comparing estimation methods for the three-parameter kappa distribution with application to precipitation data

Cited by 2 publications

References 34 publications

On bivariate modelling using a new statistical distribution with homogeneous marginals

On bivariate modelling using a new statistical distribution with homogeneous marginals

Parameter estimate for three-parameter kappa distribution using LHmoments approach

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