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Optimization of a skewed logistic di...

Finney, James Charles.

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Optimization of a skewed logistic distribution with respect to the Kolmogorov-Smirnov test.

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Optimization of a skewed logistic distribution with respect to the Kolmogorov-Smirnov test./
作者:	Finney, James Charles.
面頁冊數:	140 p.
附註:	Source: Dissertation Abstracts International, Volume: 65-07, Section: B, page: 3525.
Contained By:	Dissertation Abstracts International65-07B.
標題:	Statistics. -
電子資源:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3140246
ISBN:	0496873873

Optimization of a skewed logistic distribution with respect to the Kolmogorov-Smirnov test.
Finney, James Charles.

Optimization of a skewed logistic distribution with respect to the Kolmogorov-Smirnov test. - 140 p.

Source: Dissertation Abstracts International, Volume: 65-07, Section: B, page: 3525.

Thesis (Ph.D.)--Louisiana State University and Agricultural & Mechanical College, 2004.

The four-parameter kappa distribution (Hosking 1994) was analyzed with respect to the various possible shapes of the probability density function. The general form for the cumulative distribution function when both h and k are non-zero is: Fx=&cubl0;1- h1-kx-x /a1/k&cubr0;1/h . The parameters h and k work together to define the function's shape, xi affects location, and alpha is the scale parameter. A method of selecting parameters to minimize the Kolmogorov-Smirnov test statistic, D, was developed. The technique was first described for the logistic distribution, which is the special case of the kappa distribution with k = 0 and h = -l. Then the more general case, k = 0 and h ≠ 0, was further explored as a possibility for expanding the optimization technique. The optimization method was shown to provide the parameters h, xi, and alpha such that the Kolmogorov-Smirnov test statistic, D, was minimized. This optimization was applied to several example data sets and found to produce distributions that fit the empirical data much better than the normal or lognormal distribution functions. The results have potential applications in describing the distributions of many types of real data, including, but not limited to, weather, hydrologic and other environmental data. Matching empirical data to an invertible probability distribution makes it convenient to simulate random data that follow closely the characteristics of the natural data. Preliminary inquiry suggested that the technique might be expanded to allow non-zero values of k. This would improve the shape flexibility slightly and produce slightly better fits to empirical data.

ISBN: 0496873873Subjects--Topical Terms:

517247
Statistics.

Optimization of a skewed logistic distribution with respect to the Kolmogorov-Smirnov test.
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520 $a The four-parameter kappa distribution (Hosking 1994) was analyzed with respect to the various possible shapes of the probability density function. The general form for the cumulative distribution function when both h and k are non-zero is: Fx=&cubl0;1- h1-kx-x /a1/k&cubr0;1/h . The parameters h and k work together to define the function's shape, xi affects location, and alpha is the scale parameter. A method of selecting parameters to minimize the Kolmogorov-Smirnov test statistic, D, was developed. The technique was first described for the logistic distribution, which is the special case of the kappa distribution with k = 0 and h = -l. Then the more general case, k = 0 and h ≠ 0, was further explored as a possibility for expanding the optimization technique. The optimization method was shown to provide the parameters h, xi, and alpha such that the Kolmogorov-Smirnov test statistic, D, was minimized. This optimization was applied to several example data sets and found to produce distributions that fit the empirical data much better than the normal or lognormal distribution functions. The results have potential applications in describing the distributions of many types of real data, including, but not limited to, weather, hydrologic and other environmental data. Matching empirical data to an invertible probability distribution makes it convenient to simulate random data that follow closely the characteristics of the natural data. Preliminary inquiry suggested that the technique might be expanded to allow non-zero values of k. This would improve the shape flexibility slightly and produce slightly better fits to empirical data.
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