On some properties and application of the transformed version of a probability model defined on the unit interval

Abstract

Through this paper, the exponentiation transformation has been applied to a version of the Unit Lindley distribution having support on (0, 1). The graphical behaviour of the density curve for different values of the parameters is studied and various statistical properties of the distribution such as descriptive statistics, generating functions, reliability properties, distributions of the order statistics are discussed. Random numbers from the proposed distribution are generated and a simulation study is performed to assess the behaviour of the parameter estimates on the basis of the generated sample. The parameters of the distribution are estimated using the maximum likelihood method. Finally, the utility of the developed model is exhibited through an original data set on timing of infant deaths.