Abstract
In this article we transmute the half logistic distribution using quadratic rank transmutation map to develop a transmuted half logistic distribution. The quadratic rank transmutation map enables the introduction of extra parameter into its baseline distribution to enhance more flexibility in the analysis of data in various disciplines such as reliability analysis in engineering, survival analysis, medicine, biological sciences, actuarial science, finance and insurance. The mathematical properties such as moments, quantile, mean, median, variance, skewness and kurtosis of this distribution are discussed. The reliability and hazard functions of the transmuted half logistic distribution are obtained. The probability density functions of the minimum and maximum order statistics of the transmuted half logistic distribution are established and the relationships between the probability density functions of the minimum and maximum order statistics of the parent model and the probability density function of the transmuted half logistic distribution are considered. The parameter estimation is done by the method of maximum likelihood estimation. The flexibility of the model in statistical data analysis and its applicability is demonstrated by using it to fit relevant data. The study is concluded by demonstrating that the transmuted half logistic distribution has a better goodness of fit than its parent model. We hope this model will serve as an alternative to the existing ones in the literature in fitting positive real data.
Highlights
Half logistic probability model has a lot of applications in the analysis of survival data and other disciplines such as economics, biological sciences, insurance and finance
The half logistic distribution which was studied by Balakrishnan [1] and Balakrishnan and Puthenpura [2] has the probability density function given by Transmutation of distributions gained popularity over a decade ago from the work of Shaw et al [6] to the work of, Aryal and Tsokos [7], Aryal and Tsokos [8], Merovci et al [9], Merovci [10], Merovci and Elbata [11], Merovci and Puka [12], Granzoto et al [13], Rahman et al [14], to mention a few
The maximum likelihood estimates of the parameters, Q;7 that are inherent within the transmuted half logistic distribution function are given by the following: Let . ,. , ... .i be a sample of size n from a transmuted half logistic distribution
Summary
Email address: To cite this article: Adeyinka Femi Samuel, Olapade Akintayo Kehinde. A Study on Transmuted Half Logistic Distribution: Properties and Application. International Journal of Statistical Distributions and Applications. Vol 5, No 3, 2019, pp. 54-59. doi: 10.11648/j.ijsd.20190503.12
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