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A skewed truncated Cauchy uniform distribution and its moments


Ashani, Zahra Nazemi and Abu Bakar, Mohd Rizam and Ibrahim, Noor Akma and Adam, Mohd Bakri (2016) A skewed truncated Cauchy uniform distribution and its moments. Modern Applied Science, 10 (7). 174 - 182. ISSN 1913-1844; ESSN: 1913-1852


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.

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Additional Metadata

Item Type: Article
Divisions: Faculty of Science
Institute for Mathematical Research
DOI Number: https://doi.org/10.5539/mas.v10n7p174
Publisher: Canadian Center of Science and Education
Keywords: Skew symmetric distribution; Truncated cauchy distribution; Uniform distribution
Depositing User: Mohd Hafiz Che Mahasan
Date Deposited: 12 Jun 2018 08:20
Last Modified: 12 Jun 2018 08:20
Altmetrics: http://www.altmetric.com/details.php?domain=psasir.upm.edu.my&doi=10.5539/mas.v10n7p174
URI: http://psasir.upm.edu.my/id/eprint/54940
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