الفهرس 
Hazard rate function
Log-General Family of DistributionsOnly 14 pages are availabe for public view
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Abstract
There are many distributions for modeling lifetime data, although they do not provide enough exibility for analyzing various types of lifetime data especially in medicine and laboratory experiments. Several extensions of some well-known lifetime distributions have been developed during the last two decades for modeling and analyzing many types of real-life data that having di erent random nature. This development s followed by many approaches for generating new families of distribu-tions and hence the chance of modeling a large number of real-life data increases, hence there is a need for other families to capable of analyz- ing data. Therefore, we introduce a new general family of distributions.Using a submodel of this family, we t three data sets. Mathematical expression for the new general family of distributions are obtained, in-cluding shapes of probability density function (pdf) and hazard rate,quantiles, moments, moment generating function, stochastic ordering,order statistics and entropies (Renyi and Shannon). Some submodels of the family are inserted based on the baseline distributions: Exponential, Gompertz, Lindley and weight exponential distributions. Estimation of
the model parameters is justi ed by the method of maximum likelihood. Special submodel of this family is considered based on the exponential baseline distribution. A new two-parameter weighted exponential distri- bution has a deep connection with the so-called generalized exponential and logarithmic exponential distributions. Among its advantages, the corresponding probability density and hazard rate function (hrf) display quite attractive shapes for various modelling aims. Our theoretical con-tributions on the new distribution include some results on the rst-order stochastic dominance, the expression of the quantile function, expansions series for the moments, with discussions on the incomplete moment and moment generating function. The entropy and extropy are also investi- gated. An inferential work is performed on the related model; the esti- mation of parameters is justi ed by the method of maximum likelihood.
Finally, exibility of the family is illustrated by tting three practical data sets in di erent elds. Potentiality and elasticity of a submodel of the family are illustrated by tting failure times data.The thesis consists of ve chapters. Chapter 1 illustrates the basic principles and de nitions. One of the main aims of this chapter is to provid some backgrounds and reviews regarding the distributions. Also, presents an introduction about the weight function and the T-X family.