Abstract
In this paper, we introduce a new family of distributions whose probability density function is defined as a weighted sum of two probability density functions; one is defined as a warped version of the other. We focus our attention on a special case based on the exponential distribution with three parameters, a dilation transformation and a weight with polynomial decay, leading to a new life-time distribution. The explicit expressions of the moments generating function, moments and quantile function of the proposed distribution are provided. For estimating the parameters, the method of maximum likelihood estimation is used. Two applications with practical data sets are given.
Highlights
The mixture distributions arise in a wide variety of applications, including children’s heights distribution, discussed by Everitt & Hand (1981), and plasma concentration of Beta-Carotene given in Schlattmann (2009)
We introduce a new generator of distributions which generalizes the finite mixture of the pdfs f (x) and g(x)f (G(x)) by introducing a Lebesgue measurable and monotonic function w(x) with w(x) ∈ [0, 1] for any x ∈ (a, b)
We call the distribution with pdf (5) the functional weighted exponential distribution, FWE for short
Summary
The mixture distributions arise in a wide variety of applications, including children’s heights distribution, discussed by Everitt & Hand (1981), and plasma concentration of Beta-Carotene given in Schlattmann (2009). The k-component mixture distribution is defined via the following probability density function (pdf): k h(x) = pifi(x), (1) Using pdf (3) with w(x) = m(x), we can derive a new skewed family of distributions; for a given k(x), we get h(x) = 2 k(x)(m(x))2 + [1 – m (G(x))] g(x)k (G(x)) m (G(x)) , x ∈ R. We focus on a submodel of the family with three parameters based on the exponential distribution, a dilation transformation and a weight with polynomial decay, called the functional weighted exponential distribution.
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