Abstract
A goal of this research is providing new probability distribution called Sinh inverted exponential distribution. The new distribution was extensively depending on the hyperbolic sine family of distributions with exponential distribution as a baseline distribution. Valuable statistical properties of the proposed distribution including mathematical and asymptotic expressions for its probability density function and Reliability. Moments, quantiles, moment generating function, failure rate function, mean residual lifetime, order statistics and entropies are derived. Actually, the applicability and validation of this model is proved in simulation study and an application to neck cancer disease data.
Highlights
In many applied areas such as lifetime analysis and other fields, there is strong need to develop the classical distributions
The new distribution was extensively depending on the hyperbolic sine family of distributions with exponential distribution as a baseline distribution
The applicability and validation of this model is proved in simulation study and an application to neck cancer disease data
Summary
In many applied areas such as lifetime analysis and other fields, there is strong need to develop the classical distributions. Different methods to generating new families of distributions are defined. These include; Azzalini’s skew family by Azzalini (1985), Marshal- Olkin generated family by Marshall and Olkin (1997), exponentiated generator by Gupta et al (1998), beta-G by Eugene et al (2002). G(x) and g(x) are the CDF and PDF for any random variable, respectively and the hyperbolic sine function (sinh (x)) is defined as sinh(x) 1 ex e x. We will take G(x) is the CDF of the inverse exponential distribution and g(x) its PDF. Dey (2007) studied the inverse exponential (IE) distribution with CDF and PDF are given by We will take G(x) is the CDF of the inverse exponential distribution and g(x) its PDF. Dey (2007) studied the inverse exponential (IE) distribution with CDF and PDF are given by
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