Abstract
The statistical parameters of five generalizations of the Lindley distribution, such as the average, variance and moments, are reviewed. A new double truncated Lindley distribution with three parameters is derived. The new distributions are applied to model the initial mass function for stars.
Highlights
In recent years the Lindley distribution has been the subject of many generalizations, we report some of them among others: one with two parameters [3], a two-parameter weighted one [4], the generalized Poisson-Lindley [5], the extended Lindley [6]
[9] and the first application to astrophysics of the Lindley distribution has been done for the initial mass function (IMF) for stars and the luminosity function for galaxies [10]
Can a Lindley distribution or a generalization be an alternative to the lognormal fit for the IMF? In order to answer the above question Section 2 reviews the notion of statistical sample and Lindley distribution, Section 3 reviews five generalizations of the Lindley distribution, Section 4 introduces the double Lindley distribution and Section 5 fits the six new Lindley distributions to four samples for the mass of the stars
Summary
[2], has one parameter. Lindley distribution has been the subject of many generalizations, we report some of them among others: one with two parameters [3], a two-parameter weighted one [4], the generalized Poisson-Lindley [5], the extended Lindley [6]. Several generalizations of the Lindley distribution can be found in a recent review [8]. [9] and the first application to astrophysics of the Lindley distribution has been done for the initial mass function (IMF) for stars and the luminosity function for galaxies [10]. The IMF is routinely modeled by the lognormal distribution and the following question naturally arises. Can a Lindley distribution or a generalization be an alternative to the lognormal fit for the IMF? Can a Lindley distribution or a generalization be an alternative to the lognormal fit for the IMF? In order to answer the above question Section 2 reviews the notion of statistical sample and Lindley distribution, Section 3 reviews five generalizations of the Lindley distribution, Section 4 introduces the double Lindley distribution and Section 5 fits the six new Lindley distributions to four samples for the mass of the stars
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