Far East Journal of Theoretical Statistics
Volume 51, Issue 3, Pages 87 - 101
(November 2015) http://dx.doi.org/10.17654/FJTSNov2015_087_101 |
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COHERENT FORM OF THE NON-CENTRALITY PARAMETER IN NON-CENTRAL DISTRIBUTION
Mohammad Shaha Alam Patwary and Mezbahur Rahman
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Abstract: Apart from the theoretical contributions, non-central chi-squared distribution has been applied in mathematical physics, social and behavioral research, communication theory, management science and many other diversified research areas. Non-central chi-squared distribution has been derived mostly by considering the non-centrality parameter and sometimes by taking the non-centrality parameter Here we also consider an alternative non-centrality parameter We calculated the parametric characteristics for each of the three densities using cumulant generating function and recurrence relation. Finally, we made a head-to-head comparison among the characteristics obtained from these three unique densities. It is found that only second non-centrality parameter gives us exact correspondence in parametric characteristics calculated using both the methods of calculation. |
Keywords and phrases: cumulants, kurtosis, moment generating function, non-central beta distribution, non-central F distribution, non-central family of densities, non-central t distribution, skewness. |
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