Abstract
In this paper, a new class of continuous distributions with two extra positive parameters is introduced and is called the Type II General Exponential (TIIGE) distribution. Some special models are presented. Asymptotics, explicit expressions for the ordinary and incomplete moments, moment residual life, reversed residual life, quantile and generating functions and stress-strengh reliability function are derived. Characterizations of this family are obtained based on truncated moments, hazard function, conditional expectation of certain functions of the random variable are obtained. The performance of the maximum likelihood estimators in terms of biases, mean squared errors and confidence interval length is examined by means of a simulation study. Two real data sets are used to illustrate the application of the proposed class.
Highlights
Several families of continuous univariate distributions have been constructed by extending common families of continuous models
The basic motivations for using the Type II General Exponential (TIIGE)-G family in practice are: (i) to make the kurtosis more flexible compared to the baseline model; (ii) to produce a skewness for symmetrical distributions; (iii) to construct heavy-tailed distributions that are not longertailed for modeling real data; (iv) to generate distributions with symmetric, left-skewed, right-skewed and reversed-J shaped; (v) to define special models with all types of the hrf; and (vi) to provide consistently better fits than other generated models under the same baseline distribution
Let a = inf{x|F(x) > 0}. the asymptotics of cdf, pdf and hrf as x → a are given by F(x)~αλG(x)asx → a, f(x)~αλg(x)asx → a, h(x)~αλg(x)asx → a
Summary
Several families of continuous univariate distributions have been constructed by extending common families of continuous models. Gupta et al (1998) proposed the exponentiated-G class, which consists of raising the cumulative distribution function (cdf) to a positive power parameter. The basic motivations for using the TIIGE-G family in practice are: (i) to make the kurtosis more flexible compared to the baseline model; (ii) to produce a skewness for symmetrical distributions; (iii) to construct heavy-tailed distributions that are not longertailed for modeling real data; (iv) to generate distributions with symmetric, left-skewed, right-skewed and reversed-J shaped; (v) to define special models with all types of the hrf; and (vi) to provide consistently better fits than other generated models under the same baseline distribution.
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