Abstract
This paper proposes a new probability distribution, which belongs a member of the exponential family, defined on (0,1) unit interval. The new unit model has been defined by relation of a random variable defined on unbounded interval with respect to standard logistic function. Some basic statistical properties of newly defined distribution are derived and studied. The different estimation methods and some inferences for the model parameters have been derived. We assess the performance of the estimators of these estimation methods based on the three different simulation scenarios. The analysis of three real data examples which one is related to the coronavirus data, show better fit of proposed distribution than many known distributions on the unit interval under some comparing criteria.
Highlights
Johnson (1949) has pioneered a general system of the continuous distribution based on some transformations of the standard normal random variable
The aim of this study is to propose a new alternative unit distribution, which belongs to the exponential family, to model of the percentages and proportions
A new alternative unit distribution belongs to exponential family is introduced
Summary
Johnson (1949) has pioneered a general system of the continuous distribution based on some transformations of the standard normal random variable (rv). Y = g−1 (Z−μ), σ where g−1(⋅) is the any suitable function and μ ∈ R and σ > 0 are the parameters. Three important systems such as log-normal, unbounded (unbounded support) and bounded (unit support) have been defined by the author. Following g functions have been used g(y) = logy, g(y) = log[y/(1 − y)] and g(y) = sinh−1[y] = log[y + √1 + y2] for the log-normal (Johnson SL), bounded (Johnson SB) and unbounded (Johnson SU) systems respectively by the author, where sinh−1[t], t ∈ R is the inverse of the hyperbolic sine function. The probability density function (pdf) of the unbounded Johnson distribution system, Johnson SU, is given by fSU (y, μ, σ)
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