Abstract
<p>Although usually normal distribution is considered for statistical analysis, however in many practical situations, distribution of data is asymmetric and using the normal distribution is not appropriate for modeling the data. Base on this fact, skew symmetric distributions have been introduced. In this article, between skew distributions, we consider the skew Cauchy symmetric distributions because this family of distributions doesn't have finite moments of all orders. We focus on skew Cauchy uniform distribution and generate the skew probability distribution function of the form , where is truncated Cauchy distribution and is the distribution function of uniform distribution. The finite moments of all orders and distribution function for this new density function are provided. At the end, we illustrate this model using exchange rate data and show, according to the maximum likelihood method, this model is a better model than skew Cauchy distribution. Also the range of skewness and kurtosis for and the graphical illustrations are provided.</p>
Highlights
Skew symmetric distributions have been an attentive topic for many statistical researchers in the past few years
The rest of this article is delivered as follows: In section 2 we introduce the basic of skew truncated Cauchy uniform distribution and its cumulative distribution function
We focus on skew Cauchy uniform distribution and try to find finite moments of all orders
Summary
Skew symmetric distributions have been an attentive topic for many statistical researchers in the past few years. Gupta et al (2002) introduced new models of skew symmetric distribution, where and are replaced with the pdf and cdf of normal, student’s t, logistic, Cauchy, Laplace and uniform distribution They introduced some of their properties like characteristic function and their moments. Johnson and Kotz (1970) introduced the truncated Cauchy distribution (1) for solving the problems of the Cauchy distribution They provided its cumulative distribution function as follows: arctan ( )=. There were not finite moments of all orders for skew distribution with Cauchy kernel They tried to solve the distribution problems and make it more applicable in different areas.
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