Symmetric Generalized Logistic Distribution: Some Moment Properties and Approximation to the Normal Distribution

Abstract

In this paper we discuss some moment properties of a symmetric generalized logistic distribution indexed by a shape parameter λ and denoted by GL(λ, λ), and show that it is asymptotically normal as λ → ∞, and asymptotically double exponential as λ → 0. We also show that GL(λ, λ) can be used to approximate the normal distribution. The proposed approximation is illustrated for specific values of λ.

Keywords:

• AMS 1980 subject classification
• Primary 62H10
• secondary 65D20

Keywords:

• Logistic distribution
• normal distribution
• incomplete beta function
• shape parameter
• cumulants
• binomial probabilities
• approximation