الفهرس 
Transmuted Kumaraswamy Logistic DistributionOnly 14 pages are availabe for public view
 |  | from | 147 |  |  |
| | | from | 147 | | |
Abstract
In many applied sciences such as medicine, engineering and finance, amongst others, modeling and analyzing lifetime data is crucial. Several lifetime distributions have been used to model such kind of data. The quality of the procedures used in a statistical analysis depends heavily on the assumed probability model or distribution. Because of this, considerable effort has been expended in the development of large classes of standard probability distributions along with relevant statistical methodologies. However, there exist times when the real data do not follow any of the classical or standard probability models. So we present different types of generalized distributions and hope that the proposed models can be used effectively as competitive models to fit real data.
The simplicity of the logistic distribution and its importance as a growth curve has made it one of the many important statistical distributions. The logistic distribution is often used ”as an approximation to other symmetrical distributions due to the mathematical tractability of its cumulative distribution function”.
In order to improve the fit of the logistic model for bioassay and quintal response data, many generalized types of the logistic distribution have been proposed recently. These generalized distributions (indexed by one or more shape parameters) are developed to extend the scope of the logistic model to asymmetric probability curves and to improve the fit in the non-central probability regions. So, in this thesis, we generalize the Logistic distribution via Kumaraswamy distribution and the quadratic rank transmutation map in Chapter (1), via the Weibull-G family distribution and the quadratic rank transmutation map in Chapter (2), via the new generalized inverse Weibull-G family and the quadratic rank transmutation map in Chapter (3) and via the modified Weibull distribution and the exponential generator in Chapter (4).
The thesis is organized as follows.
In Chapter (1), a complete study of the transmuted Kumaraswamy Logistic distribution is proposed. Some basic properties of this distribution, such as quantile function, characteristic function and entropy are derived, as well as the derivation of maximum likelihood estimates of the parameters and the information matrix. Real life data is used as an application to this distribution with a comparison with other distributions to illustrate the flexibility and ability to model lifetime data. Also, a simulation study is conducted to demonstrate the effect of the sample on the estimates of the parameters. The results of this chapter are published in “Eph- International journal of Mathematics and Statistics”.
Chapter (2), deals with a complete study of the transmuted Weibull Logistic distribution, introducing some basic properties of this distribution, such as quantile function, mode, characteristic function and entropy, as well as the derivation of maximum likelihood estimators of the parameters and the information matrix. Real life data is used as an application to this distribution with a comparison with other distributions. Also, a simulation study is conducted to demonstrate the effect of the sample on the estimates of the parameters. The results of this chapter are published in “International journal of Innovative Research & Development”.
In Chapter (3), we discuss the six parameter Transmuted New Generalized Inverse Weibull Logistic distribution and discuss the usefulness of this model giving an application to reliability data. This extended model has upside-down hazard rate function and provides an alternative model to existing lifetime distributions. Various structural properties of the new distribution are derived that include explicit expressions for the r^th moment and characteristic function besides an approximate form for the quantile function. The estimation of model parameters is performed by the method of maximum likelihood, followed by a simulation study. The results of this chapter are submitted.
In Chapter (4), we introduce a new distribution named Exponential Modified Weibull logistic distribution. This distribution generalizes the following distributions: (1) Linear Failure Rate Logistic Distribution, (2) Weibull Logistic Distribution, (3) Rayleigh Logistic Distribution, (4) Exponential Logistic Distribution, where the failure rate, Weibull, Rayleigh and exponential distributions are the distributions most used for analyzing lifetime data. The properties of the proposed distribution are derived that include expressions for the r^th moment, characteristic function and quantile function. The estimation of model parameters is performed by the method of maximum likelihood and hence performing simulation study. The results of this chapter are published in “Eph- International journal of Mathematics and Statistics”.
In Chapter (5), we compare the performance of the estimators under consideration through four real data sets for the distributions defined in Chapter (1), (2), (3) and (4). We fit data for the survival times of breast cancer patients, the fatigue time of aluminum coupons, the time to breakdown of an insulating fluid between electrodes, the time to breakdown of an insulating fluid in section and times for the air conditioning system of an aircraft, concluding that the proposed models can be used quite effectively as a competitive models in analyzing data.