Generalisation Of The Inverse Exponential Distribution: Statistical Properties And Applications

ABSTRACT

There are several real life data sets that do not follow the Normal distribution; these category of data sets are either negatively or positively skewed. However, some could be slightly skewed while others could be heavily skewed. Meanwhile, most of the existing standard theoretical distributions are deficient in terms of performance when applied to data sets that are heavily skewed. To this end, the aim of this study is to extend the Inverse Exponential distribution by inducing it with skewness with a view to enhancing its efficiency. This was achieved by generalising the Inverse Exponential distribution using four different generalised families of distributions. The resulting generalised distributions are: the Kumaraswamy Inverse Exponential (KIE), Transmuted Inverse Exponential (TIE), Exponentiated Generalised Inverse Exponential (EGIE) and Weibull Inverse Exponential (WIE) distributions. Explicit expressions for the densities and basic statistical properties of these compound distributions were established, the method of maximum likelihood estimation (MLE) was used in estimating the unknown parameters and these distributions were fitted to twelve (12) real life data sets to assess their flexibility. R software was adopted and used to perform all the analyses in this study. In addition, a new generalised family of distributions named the Exponential Generalised family of distributions has been defined and explored. Part of the main results in this study include a statistical table that was generated for the Inverse Exponential distribution. A simulation study was also conducted and it was concluded that the standard error and biasedness generated by the parameters of the Exponential Inverse Exponential distribution became small as the sample size increases. Excerpt from the analysis indicates that the derived generalised distributions are more flexible than their sub-models but for the exception of data sets with large variance and outliers. It is recommended that more link functions that will result in generalised families of distributions with only one additional shape parameter and void of special functions should be developed.