Abstract
In this paper, we modify the Mahmoud and Mandouh (2013) model by adopting double truncation technique. It is referred to as Double Truncated Transmuted Frechet (DTTF) distribution. Diverse probabilistic and reliability measures are developed and discussed. The MLEs of parameters are derived and a simulation study is also made. The DTTF distribution is modeled by two real-time datasets and supportive rationalized results provide the evidence that DTTF distribution is a reasonably better fit model than its competing models. Keywords: Frechet Distribution, Double Truncation, Hazard Function, Moments, MLE, Quadratic Rank Transmutation Map (QRTM), Renyi entropy, Order Statistics. DOI : 10.7176/MTM/9-3-02 Publication date : March 31 st 2019
Highlights
The Double Truncated Transmuted Fréchet (DTTF) distribution is modeled by two real-time datasets and supportive rationalized results provide the evidence that DTTF distribution is a reasonably better fit model than its competing models
In numerous continuous probability distributions, extreme value theory is an important part of statistical literature and one of the special cases is Fréchet distribution
Cumulants generating function based on a relation between ordinary moments and cumulants is defined as r−1 r − 1 K r = μr − ∑ (i − 1) Ki μr−i i=1 cumulants generating function of DTTF distribution can be written as r αβ(1 + −C
Summary
In numerous continuous probability distributions, extreme value theory is an important part of statistical literature and one of the special cases (inverse Weibull, inverse Rayleigh, inverse Exponential or Gumbel type-II) is Fréchet distribution. Transmuted Marshall Oklin Fréchet distribution introduced in Kumaraswamy family of distributions by Yousof et al (2016) They developed its application in carbon fiber and glass fiber datasets. Mansour et al (2018) generalized the Fréchet distribution in Odd Lindley family of distributions They illustrated its application in exceedances of flood peaks and the breaking stress of carbon fibers datasets. Scientific literature extended by Mahmoud and Mandouh (2013) when they generalized the Fréchet distribution in QRTM family of distributions and developed its application in breaking stress of carbon fiber and simulated datasets. Afify et al (2015) investigated Marshall Olkin Fréchet distribution in QRTM family of distributions and discussed its application in breaking stress of carbon fibers and strength of 1.5cm glass fibers datasets. Fig.[1] and Fig.[2] illustrate the reasonable shapes of CDF and PDF for selected values of the parameters α, β and λ
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