Abstract
We propose a new generator of continuous distributions with one extra positive parameter called the odd Lindley-G family. Some special cases are presented. The new density function can be expressed as a linear combination of exponentiated densities based on the same baseline distribution. Various structural properties of the new family, which hold for any baseline model, are derived including explicit expressions for the quantile function, ordinary and incomplete moments, generating function, Renyi entropy, reliability, order statistics and their moments and k upper record values. We discuss estimation of the model parameters by maximum likelihood and provide an application to a real data set.
Highlights
In recent years, several ways of generating new distributions from classic ones has attracted theoretical and applied statisticians due to their flexible properties
A range of mathematical properties of Equation (5) is derived in Section 3 including a useful expansion for the pdf and explicit expressions for the moments and generating function
Some structural properties of the new family such as the ordinary and incomplete moments and generating function can be determined from well-established properties of the Exp-G distributions
Summary
Several ways of generating new distributions from classic ones has attracted theoretical and applied statisticians due to their flexible properties. Ghitany, Atieh, and Nadarajah (2008) showed through a numerical example that the hazard function of the Lindley distribution does not exhibit a constant hazard rate, indicating its flexibility over the exponential distribution It has recently received considerable attention as an appropriate model to analyze lifetime data especially in applications modeling stress-strength reliability; see, for example, Ghitany et al (2008), Zakerzadeh and Dolati (2009), Mazucheli and Achcar (2011), Gupta and Singh (2012), Warahena-Liyanage and Pararai (2014). A range of mathematical properties of Equation (5) is derived in Section 3 including a useful expansion for the pdf and explicit expressions for the moments and generating function.
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