When the weight function depends on the
lengths of the units of interest, the resulting distribution is called length
biased. Length biased distribution is thus a special case of the more general
form, known as weighted distribution. In this paper, a new three parameter
probability distribution called the Weibull Length Biased Exponential
distribution is proposed, its statistical properties are studied in minute
details. Expansions of the density function of the WLBE Distribution,
reliability analysis, asymptotic behavior, moments etc. are discussed in minute
details. Maximum likelihood estimation method is employed to determine the
estimate of the parameters of the proposed distribution. Simulation studies and
application to two life time data is performed to determine the flexibility of
the model in modeling lifetime data.
Keywords: Weibull generalized
family of distribution, length biased exponential distribution, moments,
maximum likelihood, fitted models.