Abstract
In this paper, a three-parameter continuous distribution, namely, Inverted Beta-Lindley (IBL) distribution is proposed and studied. The new model turns out to be quite flexible for analyzing positive data and has various shapes of density and hazard rate functions. Several statistical properties associated with this distribution are derived. Moreover, point estimation via method of moments and maximum likelihood method are studied and the observed information matrix is derived. An application of the new model to real data shows that it can give consistently a better fit than other important lifetime models.
Highlights
The beta distribution with support in the standard unit interval (0, 1) has been utilized extensively in statistical theory and practice for over 100 years
McDonald and Bookstaber [10] have developed an option pricing formula based on this distribution that includes the widely used Black Scholes formula based on the assumption of log-normally distributed returns
We introduce a new distribution having three parameters which is based on mixing the inverted beta distribution and Lindley distributions, so-called the Inverted Beta Lindley distribution (IBL)
Summary
The beta distribution with support in the standard unit interval (0, 1) has been utilized extensively in statistical theory and practice for over 100 years. It is very versatile and a variety of uncertainties can be usefully modeled by this distribution, since it can take an amazingly great variety of forms depending on the values of its parameters. The distributional properties of IBL distribution including the hazard and survival functions, the behavior of the probability density function, mean residual life and reversed failure rate, the moments and the associated moments, Lorenz and Bonferroni curves and .
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