Generalized Truncated Fr閏het Generated Family Distributions and Their Applications

ZeinEldin, Ramadan A.; Chesneau, Christophe; Jamal, Farrukh; Elgarhy, Mohammed; Almarashi, Abdullah M.; Al-Marzouki, Sanaa

doi:10.32604/cmes.2021.012169

Cited by 13 publications

(5 citation statements)

References 22 publications

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“…The following points provide sufficient incentive to study the proposed model. We specify it as follows: (i) we employed a unique transformation to develop UPWD instead of employing traditional transformation found in literature to propose unit distributions which include Y = e −x , ð1 + xÞ −1 , or Y = ðxÞð1 + xÞ −1 , depending upon the functional identifiability of the baseline model; (ii) recent developments in distribution theory have shown a significant rise in the analysis of bivariate extensions of univariate models; for further information, we may refer the readers to see in [17][18][19][20]. So, we introduced and thoroughly explored a bivariate extension of a unit distribution, known as the bivariate unit-power Weibull distribution (BIUPWD for short) as far as no bivariate extension has been explored for the unit distributions in the literature.…”

Section: Introductionmentioning

confidence: 99%

Statistical Analysis of COVID-19 Data: Using A New Univariate and Bivariate Statistical Model

Bantan

Shafiq

Tahir

et al. 2022

Journal of Function Spaces

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In this paper, a new distribution named as unit-power Weibull distribution (UPWD) defined on interval (0,1) is introduced using an appropriate transformation to the positive random variable of the Weibull distribution. This work offers quantile function, linear representation of the density, ordinary and incomplete moments, moment-generating function, probability-weighted moments, L -moments, TL-moments, Rényi entropy, and MLE estimation. Additionally, several actuarial measures are computed. The real data applications are carried out to underline the practical usefulness of the model. In addition, a bivariate extension for the univariate power Weibull distribution named as bivariate unit-power Weibull distribution (BIUPWD) is also configured. To elucidate the bivariate extension, simulation analysis and application using COVID-19-associated fatality rate data from Italy and Belgium to conform a BIUPW distribution with visual depictions are also presented.

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Section: Introductionmentioning

confidence: 99%

Statistical Analysis of COVID-19 Data: Using A New Univariate and Bivariate Statistical Model

Bantan

Shafiq

Tahir

et al. 2022

Journal of Function Spaces

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“…In the last years, many statisticians are attracted by the generated families of distributions, such as Kumaraswamy-G [1], T-X family [2], sine-G [3], Type II half logistic-G [4], exponentiated extended, Muth, odd Frèchet-G [5][6][7], truncated Cauchy power-G [8], transmuted odd Fréchet-G [9], exponentiated M-G [10], Topp-Leone odd Fréchet-G [11], Sine Topp-Leone-G [12], and generalized truncated Fréchet-G [13].…”

Section: Introductionmentioning

confidence: 99%

Sine Power Lindley Distribution with Applications

Almarashi¹

2022

Intelligent Automation &Amp; Soft Computing

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Sine power Lindley distribution (SPLi), a new distribution with two parameters that extends the Lindley model, is introduced and studied in this paper. The SPLi distribution is more flexible than the power Lindley distribution, and we show that in the application part. The statistical properties of the proposed distribution are calculated, including the quantile function, moments, moment generating function, upper incomplete moment, and lower incomplete moment. Meanwhile, some numerical values of the mean, variance, skewness, and kurtosis of the SPLi distribution are obtained. Besides, the SPLi distribution is evaluated by different measures of entropy such as Rényi entropy, Havrda and Charvat entropy, Arimoto entropy, Arimoto entropy, and Tsallis entropy. Moreover, the maximum likelihood method is exploited to estimate the parameters of the SPLi distribution. The applications of the SPLi distribution to two real data sets illustrate the flexibility of the SPLi distribution, and the superiority of the SPLi distribution over some well-known distributions, including the alpha power transformed Lindley, power Lindley, extended Lindley, Lindley, and inverse Lindley distributions.

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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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Generalized Truncated Fr閏het Generated Family Distributions and Their Applications

Cited by 13 publications

References 22 publications

Statistical Analysis of COVID-19 Data: Using A New Univariate and Bivariate Statistical Model

Statistical Analysis of COVID-19 Data: Using A New Univariate and Bivariate Statistical Model

Sine Power Lindley Distribution with Applications

Harmonic Mixture Fréchet Distribution: Properties and Applications to Lifetime Data

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