Generalized Lehmann Alternative Type II Family of Distributions and Their Applications
Lehmann Alternative Type II Family of Distributions
Keywords:Lehmann Alternative, Entropy, Hazard rate function, Kumaraswamy distribution, Marshall-Olkin distribution, Record value
A new generalized family called Generalized Lehmann Alternative Type II (GLA2) family is introduced and studied in this paper. Special cases of this family using Uniform and Kumaraswamy distributions as base are developed and their statistical properties studied. Generalized Lehmann Alternative Type II Exponential (GLA2E) distribution is also developed and its statistical properties are obtained along with application. The new distribution is applied to a real data set to show the effectiveness of the distribution and it is verified that the new model is a better model than the existing exponential model and Marshall-Olkin extended exponential model. A detailed study on the record value theory associated with GLA2E distribution is conducted. Using the mean, variance and covariance of upper record values of the extended model, BLUE’s of location and scale parameters are obtained and future records are predicted which has a number of practical uses. The 95% confidence interval for location and scale parameters are also computed. The result is applied to a real data set to validate the results. Entropy of record values is derived. This result will be useful in characterization of record values based on entropies and a quantification of information contained in each additional record value based on entropy measure.