Extended Poisson Fréchet Distribution and its Applications

Khalil, Mohamed G.; Rezk, Hoda

doi:10.18187/pjsor.v15i4.2660

Cited by 3 publications

(2 citation statements)

References 3 publications

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“…Several extensions of the Fréchet distribution have been proposed in the literature aimed at making it more exible in modelling both monotonic and non-monotonic datasets. Some extensions of the Fréchet distribution include the Burr X Fréchet (BRXFR) [2], the odd Lomax Fréchet (OLXF) [3], the Poisson-Fréchet (POF) [4], the new exponential-X Fréchet (NEXF) [5], the Weibull Fréchet (WFR) [6], extended Poisson Fréchet distribution (P-BX-Fr) [7], the Burr XII Fréchet (BrXIIFr) [8], the modi ed Fréchet-Rayleigh distribution (MFRD) [9], truncated Weibull Fréchet distribution (TWFr) [10,11], the Marshall-Olkin Fréchet distribution (MOF) [12], the gamma extended Fréchet distribution (GEF) [13], the Lehmann type II Fréchet Poisson distribution (LFP) [14], the exponential transmuted Fréchet distribution (ETF) [15], the modi ed Fréchet (MF) [16], the generalised truncated Fréchet generated family distributions (TGFr-G) [17], and the double truncated transmuted Fréchet distribution (DTTF) [18]. Not long ago, [19] proposed a new family of mixture distribution using the weighted harmonic means of two survival functions and called it the harmonic mixture-G (HMG) family.…”

Section: Introductionmentioning

confidence: 99%

Harmonic Mixture Fréchet Distribution: Properties and Applications to Lifetime Data

Ocloo

Brew

Nasiru³

et al. 2022

International Journal of Mathematics and Mathematical Sciences

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In this study, we propose a four-parameter probability distribution called the harmonic mixture Fréchet. Some useful expansions and statistical properties such as moments, incomplete moments, quantile functions, entropy, mean deviation, median deviation, mean residual life, moment-generating function, and stress-strength reliability are presented. Estimators for the parameters of the harmonic mixture Fréchet distribution are derived using the estimation techniques such as the maximum-likelihood estimation, the ordinary least-squares estimation, the weighted least-squares estimation, the Cramér–von Mises estimation, and the Anderson–Darling estimation. A simulation study was conducted to assess the biases and mean square errors of the estimators. The new distribution was applied to three-lifetime datasets and compared with the classical Fréchet distribution and eight (8) other extensions of the Fréchet distribution.

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Section: Introductionmentioning

confidence: 99%

Harmonic Mixture Fréchet Distribution: Properties and Applications to Lifetime Data

Ocloo

Brew

Nasiru³

et al. 2022

International Journal of Mathematics and Mathematical Sciences

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“…The exponential Weibull-Poisson distribution which generalises the distribution was derived and studied by Barreto-Souza and Cribari-Neto (2009). The Kumaraswamy Lindley-Poisson distribution which generalises the Lindley-Poisson distribution was studied by Pararai et al (2015), Mohamed and Rezk (2019) developed and studied the properties and applications of the extended Poisson-Frechet distribution.…”

Section: Introductionmentioning

confidence: 99%

Lehmann Type II Frechet Poisson Distribution: Properties, Inference and Applications as a Life Time Distribution

Ogunde¹,

Olalude²,

Adeniji³

et al. 2021

IJSP

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A new generalization of the Frechet distribution called Lehmann Type II Frechet Poisson distribution is defined and studied. Various structural mathematical properties of the proposed model including ordinary moments, incomplete moments, generating functions, order statistics, Renyi entropy, stochastic ordering, Bonferroni and Lorenz curve, mean and median deviation, stress-strength parameter are investigated. The maximum likelihood method is used to estimate the model parameters. We examine the performance of the maximum likelihood method by means of a numerical simulation study. The new distribution is applied for modeling three real data sets to illustrate empirically its flexibility and tractability in modeling life time data.

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Three-parameters Gumbel Distribution: Formulation and Parameter Estimation

Okumu,

Ouno,

Karanjah

et al. 2024

IJSDA

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Modeling extreme value theories is really gaining interest in the world with scientist working to improve the flexibility of the distributions by adding parameter(s). Extreme value distributions are always described to include families of Gumbel, Weibull and Frechet distributions. Of the three distributions, Gumbel distribution is the most commonly used in the extreme value theory analysis. Existing literature has shown that the addition of parameter to a distribution makes it robust and/or more flexible hence the study intends to improve the existing two parameters Gumbel distribution using the Marshall and Olkin proposed method for introducing a new estimator/parameter to an existing distribution. The developed distribution will be important to the applications in some life time studies like high temperature, earthquakes, network designs, horse racing, queues in supermarket, insurance, winds, risk management, ozone concentration, flood, engineering and financial concepts. The parameters for the introduced distribution was estimated using Maximum Likelihood Estimation method. The introduced three parameters Gumbel distribution is a probability distribution function which can be used in modelling statistical data. The maximum likelihood estimates for the three parameters namely shape, location and dispersion are efficient, sufficient and consistent and this makes the function more flexible and better for application. The three parameters Gumbel distribution can be used in modeling and analysis of normal data, skewed data and extreme data since it will provide efficient, sufficient and consistent estimates.

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Extended Poisson Fréchet Distribution and its Applications

Cited by 3 publications

References 3 publications

Harmonic Mixture Fréchet Distribution: Properties and Applications to Lifetime Data

Harmonic Mixture Fréchet Distribution: Properties and Applications to Lifetime Data

Lehmann Type II Frechet Poisson Distribution: Properties, Inference and Applications as a Life Time Distribution

Three-parameters Gumbel Distribution: Formulation and Parameter Estimation

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