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Marshall University

1. Otunuga, Oluwaseun Elizabeth. The Pareto-g Extended Weibull Distribution.

Degree: 2017, Marshall University

URL: https://mds.marshall.edu/etd/1106

In this thesis, the Pareto family of extended Weibull distribution is introduced and discussed extensively. This family consists of the Pareto (Type I) Extended Weibull Distribution or PEW for short, and the Pareto (Type II) Extended Weibull Distribution or otherwise called the Lomax Extended Weibull Distribution or LEW for short. The numbers of the parameters of PEW or LEW depend on the number of parameters for the extended Weibull distribution and type of the Pareto distribution. Some properties of these distributions, such as the hazard rate function, the survival function, moments, skewness, kurtosis, mean deviation and entropies are discussed. The maximum likelihood estimation of the parameters and corresponding confidence intervals are also discussed. We demonstrate the applications and versatility of the distributions over some existing distributions by analyzing real-life data sets.

Subjects/Keywords: Entropies; Extended Weibull distribution; Hazard function; Lomax distribution; Maximum likelihood estimation; Pareto distribution; <; p>; Entropy.<; /p>; <; p>; Mathematical statistics.<; /p>; <; p>; Weibull distribution.<; /p>;

Record Details Similar Records

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^{th} Edition):

Otunuga, O. E. (2017). The Pareto-g Extended Weibull Distribution. (Thesis). Marshall University. Retrieved from https://mds.marshall.edu/etd/1106

Note: this citation may be lacking information needed for this citation format:

Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^{th} Edition):

Otunuga, Oluwaseun Elizabeth. “The Pareto-g Extended Weibull Distribution.” 2017. Thesis, Marshall University. Accessed October 22, 2019. https://mds.marshall.edu/etd/1106.

Note: this citation may be lacking information needed for this citation format:

Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^{th} Edition):

Otunuga, Oluwaseun Elizabeth. “The Pareto-g Extended Weibull Distribution.” 2017. Web. 22 Oct 2019.

Vancouver:

Otunuga OE. The Pareto-g Extended Weibull Distribution. [Internet] [Thesis]. Marshall University; 2017. [cited 2019 Oct 22]. Available from: https://mds.marshall.edu/etd/1106.

Note: this citation may be lacking information needed for this citation format:

Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Otunuga OE. The Pareto-g Extended Weibull Distribution. [Thesis]. Marshall University; 2017. Available from: https://mds.marshall.edu/etd/1106

Not specified: Masters Thesis or Doctoral Dissertation

Marshall University

2. Sun, Jianan. Statistical Properties of a Convoluted Beta-Weibull Distribution.

Degree: 2011, Marshall University

URL: http://mds.marshall.edu/etd/277

A new class of distributions recently developed involves the logit of the beta distribution. Among this class of distributions are the beta-normal (Eugene et.al. (2002)); beta-Gumbel (Nadarajah and Kotz (2004)); beta-exponential (Nadarajah and Kotz (2006)); beta-Weibull (Famoye et al. (2005)); beta-Rayleigh (Akinsete and Lowe (2008)); beta-Laplace (Kozubowski and Nadarajah (2008)); and beta-Pareto (Akinsete et al. (2008)), among a few others. Many useful statistical properties arising from these distributions and their applications to real life data have been discussed in the literature. One approach by which a new statistical distribution is generated is by the transformation of random variables having known distribution function(s). The focus of this work is to investigate the statistical properties of the convoluted beta-Weibull distribution, defined and extensively studied by Famoye et al. (2005). That is, if X is a random variable having the beta-Weibull distribution with parameters a1, B1, c1, y1 i.e. X=BW(a1, B1, c1 and y1) and Y has a beta-Weibull distribution expressed as Y=BW(a2, B2, c2, y2) what then is the distribution of the convolution of X and Y. That is, the distribution of the random variable Z=X+Y. We obtain the probability density function (pdf) and the cumulative distribution function (cdf) of the convoluted distribution. Various statistical properties of this distribution are obtained, including, for example, moment, moment and characteristic generating functions, hazard function, and the entropy. We propose the method of Maximum Likelihood Estimation (MLE) for estimating the parameters of the distribution. The open-source software R is used extensively in implementing our results.

Subjects/Keywords: Beta distribution; convolution; estimation; moments; simulation; Weibull distribution; <; p>; Mathematical statistics.<; /p>;

Record Details Similar Records

❌

APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^{th} Edition):

Sun, J. (2011). Statistical Properties of a Convoluted Beta-Weibull Distribution. (Thesis). Marshall University. Retrieved from http://mds.marshall.edu/etd/277

Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^{th} Edition):

Sun, Jianan. “Statistical Properties of a Convoluted Beta-Weibull Distribution.” 2011. Thesis, Marshall University. Accessed October 22, 2019. http://mds.marshall.edu/etd/277.

Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^{th} Edition):

Sun, Jianan. “Statistical Properties of a Convoluted Beta-Weibull Distribution.” 2011. Web. 22 Oct 2019.

Vancouver:

Sun J. Statistical Properties of a Convoluted Beta-Weibull Distribution. [Internet] [Thesis]. Marshall University; 2011. [cited 2019 Oct 22]. Available from: http://mds.marshall.edu/etd/277.

Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Sun J. Statistical Properties of a Convoluted Beta-Weibull Distribution. [Thesis]. Marshall University; 2011. Available from: http://mds.marshall.edu/etd/277

Not specified: Masters Thesis or Doctoral Dissertation