Abstract
In this work we focus on proposing a new lifetime Weibull type model called the transmuted Topp-Leone Weibull and studying its properties. We derive some new bivariate and multivariate transmuted Topp-Leone Weibull versions using “Farlie Gumbel Morgenstern (FGM) Copula”, “modified FGM Copula”, “Clayton Copula” and “Renyi's entropy Copula”. The estimation of its unknown parameters is carried out by considering different method of estimation. The statistical performances of all methods are studied by two real data sets and a numerical Monte Carlo simulation. The Cramer-Von Mises method is the best method for modeling the carbon fibers data. The maximum likelihood method is the best method for modeling the Leukemia data, however all other methods performed well.
Highlights
Introduction and genesisWhen a = 0 we have the one parameter Weibull model
Introduction and genesisConsider the two-parameters Weibull (W) type lifetime model with probability density function (P.D.F) and cumulative function (C.D.F) are given as ga,b(w) = babxb−1e−(aw)b, [1] andGa,b(w) = 1 − e−(aw)b, [2]Where parameter a > 0 dominate the shape of the model b > 0 is a scale parameter
The sk(W) of the proposed distribution can range in the interval (−0.68, 5.1) and this means that the new model can be left and right skewed, whereas the ku(X) of the proposed distribution varies in the interval (−398.1, 54.1)
Summary
When a = 0 we have the one parameter Weibull model. We study a new model called the transmuted Topp-Leone-. Based on the TTL-G family, we construct the new four-parameter TTL-W model. Family pioneered by Rezaei et al (2016), Yousof et al (2017b) defined the C.D.F of their transmuted Topp-Leone G (TTL-G) family by. The P.D.F of the TTL-G family is given by Transmuted Topp-Leone Weibull Lifetime Distribution: Statistical Properties and Different Method of Estimation. Theorem 1: Let T be a random variable (rv) having the well-known Exponentiated W (Exp-W) distribution with positive parameters a , b and δ. Etal., (2017) (Topp Leone generated W.), Aryal. Et al., (2017) (exponentiated transmuted W.), Yousof. Et al, (2017a) (new four-parameter W.), Brito et al, (2017) (Topp-Leone Odd Log-Logistic W.), Hamedani.
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