Abstract
In this paper, for the first time we introduce a new four-parameter model called the Gumbel- Pareto distribution by using the T-X method. We obtain some of its mathematical properties. Some structural properties of the new distribution are studied. The method of maximum likelihood is used for estimating the model parameters. Numerical illustration and an application to a real data set are given to show the flexibility and potentiality of the new model.
Highlights
Eugene et al (1) for the first time introduced the beta-generated family of distributions
“They noted that the probability density function pdf of the beta random variable and the cumulative distribution function CDF of any distribution are between 0 and 1”
Alzaatreh et al (10) presented a new general method for generating new distributions, called T-X family of distributions. This method depends on replacing the beta pdf in (1) with a pdf of any continuous random variable and applying a function W(F(x)) that satisfies the following conditions: 1- W(F(x)) ∈ [a, b] . 2- W(F(x)) is differentiable and monotonically nondecreasing. 3- W(F(x)) → a as x →−∞ and W(F(x)) → b as x →∞
Summary
Eugene et al (1) for the first time introduced the beta-generated family of distributions. Generate 1000 samples of each of sizes 10, 15,..., 30 from the GPD distribution for different values of the parameters k, λ, θ and σ, using the CDF of GPD, and the maximum likelihood estimates for each sample will be obtained, along with the mean, root of the mean square error, bias and standard error of those estimates. The steps of this procedure will be as the following: 1.
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