Award Date

1-1-2008

Degree Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Mathematical Sciences

First Committee Member

Malwane M. A. Ananda

Number of Pages

257

Abstract

Several newly formed continuous parametric distributions are introduced to analyze skewed data. Firstly, a two-parameter smooth continuous lognormal-Pareto composite distribution is introduced for modeling highly positively skewed data. The new density is a lognormal density up to an unknown threshold value and a Pareto density for the remainder. The resulting density is similar in shape to the lognormal density, yet its upper tail is larger than the lognormal density and the tail behavior is quite similar to the Pareto density. Parameter estimation methods and the goodness-of-fit criterion for the new distribution are presented. A large actuarial data set is analyzed to illustrate the better fit and applicability of the new distribution over other leading distributions. Secondly, the Odd Weibull family is introduced for modeling data with a wide variety of hazard functions. This three-parameter family is derived by considering the distributions of the odds of the Weibull and inverse Weibull families. As a result, the Odd Weibull family is not only useful for testing goodness-of-fit of the Weibull and inverse Weibull as submodels, but it is also convenient for modeling and fitting different data sets, especially in the presence of censoring and truncation. This newly formed family not only possesses all five major hazard shapes: constant, increasing, decreasing, bathtub-shaped and unimodal failure rates, but also has wide variety of density shapes. The model parameters for exact, grouped, censored and truncated data are estimated in two different ways due to the fact that the inverse transformation of the Odd Weibull family does not change its density function. Examples are provided based on survival, reliability, and environmental sciences data to illustrate the variety of density and hazard shapes by analyzing complete and incomplete data. Thirdly, the two-parameter logistic-sinh distribution is introduced for modeling highly negatively skewed data with extreme observations. The resulting family provides not only negatively skewed densities with thick tails, but also variety of monotonic density shapes. The advantages of using the proposed family are demonstrated and compared by illustrating well-known examples. Finally, the folded parametric families are introduced to model the positively skewed data with zero data values.

Keywords

Data; Distributions; Formed; Maximum Likelihood; Modeling; Pareto Density; Skewed; Skewed Data; Statistical

Controlled Subject

Statistics

File Format

pdf

File Size

6277.12 KB

Degree Grantor

University of Nevada, Las Vegas

Language

English

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