2018•American journal of mathematics and statisticsOpen access

Transmuted Stretched Exponential Distribution with Applications

Gulshan Ara Majid, Ahmad Saeed Akhter

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Abstract

In this paper, we have introduced generalization of the Stretched Exponential distribution termed as the Transmuted Stretched Exponential distribution. This suggested distribution can model data in form of decreasing and increasing hazard rates. Besides, we have derived some mathematical properties of the distribution covering probability density function, distribution function, survival, failure rate and reversed hazard functions, moments, moment generating function, incomplete moments, cumulant generating function, quantile function, mean deviation and Renyi entropy of introduced distribution. The Maximum Likelihood method has been used for estimation of parameters. We have delivered real data sets to demonstrate the worth and significance of presented distribution. It has been observed that the introduced distribution of three parameters fits better than competitive distributions for data sets.

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What this paper is about

In this paper, we have introduced generalization of the Stretched Exponential distribution termed as the Transmuted Stretched Exponential distribution. This suggested distribution can model data in form of decreasing and increasing hazard rates. Besides, we have derived some mathematical properties of the distribution covering probability density function, distribution function, survival, failure rate and reversed hazard functions, moments, moment generating function, incomplete moments, cumulant generating function, quantile function, mean deviation and Renyi entropy of introduced distribution. The Maximum Likelihood method has been used for estimation of parameters. We have delivered real data sets to demonstrate the worth and significance of presented distribution. It has been observed that the introduced distribution of three parameters fits better than competitive distributions for data sets.

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Available abstract

In this paper, we have introduced generalization of the Stretched Exponential distribution termed as the Transmuted Stretched Exponential distribution. This suggested distribution can model data in form of decreasing and increasing hazard rates. Besides, we have derived some mathematical properties of the distribution covering probability density function, distribution function, survival, failure rate and reversed hazard functions, moments, moment generating function, incomplete moments, cumulant generating function, quantile function, mean deviation and Renyi entropy of introduced distribution. The Maximum Likelihood method has been used for estimation of parameters. We have delivered real data sets to demonstrate the worth and significance of presented distribution. It has been observed that the introduced distribution of three parameters fits better than competitive distributions for data sets.

Key concepts: Mathematics, Quantile function, Exponential distribution, Log-Cauchy distribution, Moment-generating function, Distribution fitting, Natural exponential family, Exponential function

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