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Abstract
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We study general mathematical properties of a new class of continuous distributions with an extra positive
parameter called the type I half-logistic family. We present some special models and investigate the
asymptotics and shapes. The new density function can be expressed as a linear combination of exponentiated
densities based on the same baseline distribution. We derive a power series for the quantile function.
Explicit expressions for the ordinary and incomplete moments, quantile and generating functions, Bonferroni
and Lorenz curves, Shannon and Rényi entropies and order statistics are determined. We introduce
a bivariate extension of the new family. We discuss the estimation of the model parameters by maximum
likelihood and illustrate its potentiality by means of two applications to real data
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