Modified Weighted Pareto Distribution Type I (MWPDTI)

           في هذا البحث استخدمنا طريقة Azzallini لإيجاد توزيع موزون مشتق من توزيع  باريتو القياسي النوع الاول((SPDTI عن طريق إدخال معلمة الشكل ( ) الناتجة عن الطريقة المذكورة أعلاه لتغطية الفترة (0 ، 1[ التي أهملها التوزيع القياسي.وبالتالي ، فإن التوزيع المقترح هو تعديل لتوزيع باريتو من النوع الأول ، حيث تكون القيم الاحتمالية للمتغير العشوائي خلال الفترة تم ايجاد الخصائص الاحصائية لتوزيع باريتو المعدل الموزون من النوع الاول (  (MWPDTIكدالة كثافة الاحتمالة ودالة التوزيع  ودالة البقاء والعزوم والدوال الاحصائية الاخرى .In this paper, the Azzallini’s method used to find a weighted distribution derived from the standard Pareto distribution of type I (SPDTI) by inserting the shape parameter (θ) resulting from the above method to cover the period (0, 1] which was neglected by the standard distribution. Thus, the proposed distribution is a modification to the Pareto distribution of the first type, where the probability of the random variable lies within the period  The properties of the modified weighted Pareto distribution of the type I (MWPDTI) as the probability density function ,cumulative distribution function, Reliability function , Moment and  the hazard function are found. The behaviour of probability density function for MWPDTI distribution by representing the values of    This means, the probability density function of this distribution treats the period (0,1] which is ignore in SPDTI

An Extended Weighted Exponential Distribution

A new class of weighted distributions is proposed by incorporating an extended exponential distribution in Azzalini’s (1985) method. Several statistics and reliability properties of this new class of distribution are obtained. Maximum likelihood estimators of the unknown parameters cannot be obtained in explicit forms; they have to be obtained by solving some numerical methods. Two data sets are analyzed for illustrative purposes, and show that the proposed model can be used effectively in analyzing real data

Reliability Prediction Updating Through Computational Bayesian for Mixed and Non-mixed Lifetime Data Using More Flexible New Extra Modified Weibull Model

A new lifetime reliability model with four parameters is proposed. We call it the extra modified Weibull model (EMWM), which is an extension of the modified Weibull model (MWM), capable of modeling a different shapes of hazard function. The new model is developed by introducing fourth parameter in MWM called indicator parameter. The main advantage of an indicator (fourth) parameter is that it gives the new model mixture and non-mixture options, besides different shapes of hazard function including bathtub. The model parameters can be estimated based on a Bayesian generalized posterior method that serves as a tool for model identification, and it gives an efficient computational updating approach with new ways of predicting and measuring behavior. To have insight of the new indicator parameter and to see its importance, we have considered three data sets [Murthy et al [1], Badar and Priest [2], and  Aarset [3]) which have been studied in the past. A prediction updating of the earlier studies of the data sets through the generalized posterior summaries using Markov Chain Monte Carlo (MCMC) Gibbs sampling approach are presented for the proposed model for the different parameters. The behavior of the parameters would help the users to have more clarity about the role of the indicator parameter, and hence may be useful for certain sets of data. The proposed model is fully adaptive to the available failure data and gives reliability engineers and scientists another option for modeling the life time data. We provide description of the mathematical properties of the new model along with failure rate function

Comparison of Different Entropy Measures for Selected Models

In this article, the differential entropy and -entropy for Nakagami-mu distribution is derived. In addition, the differential entropy and -entropy for some selected versions of these distributions are obtained. Further, numerical comparisons are assessed to indicate which selection distribution has advantages over the other selection in terms of relative loss in entropy

Geometric skew-Cauchy distribution as an alternative to the skew-normal and geometric skew-normal distributions

Mini Dissertation (MSc (Advanced Data Analytics))--University of Pretoria, 2021.The skew-normal distribution was popularised by Azzalini [4] to model skewed data. However, the skew-normal distribution is always unimodal. Kundu [24] recently presented the geometric skew-normal distribution by considering a geometric compounding sum of normal random variables. This distribution is more flexible than the skew-normal distribution since it can be multimodal. In this dissertation we present a new distribution namely the geometric skew-Cauchy distribution. The idea follows a similar approach to that of Kundu's. The difference, however, is that we consider a geometric compounding sum of Cauchy random variables. The inclusion of a simulation and application chapter demonstrates the practical use of this new distribution. It turns out that the geometric skew-Cauchy distribution is also more flexible than the skew-normal distribution. It is concluded that this new distribution can be used as an alternative to the geometric skew-normal distribution since both distributions can be multimodal. The advantage over the geometric skew-normal distribution, is the ability of the geometric skew-Cauchy distribution to model fatter-tailed data.National Research Foundation (NRF) of South Africa, Reference: SRUG190308422768 grant No. 120839; Academic Statistics Funding Instrument grant No. 127946; SARChI Research Chair UID71199.StatisticsMSc (Advanced Data Analytics)Unrestricte

Modeling and Optimization of Stochastic Process Parameters in Complex Engineering Systems

For quality engineering researchers and practitioners, a wide number of statistical tools and techniques are available for use in the manufacturing industry. The objective or goal in applying these tools has always been to improve or optimize a product or process in terms of efficiency, production cost, or product quality. While tremendous progress has been made in the design of quality optimization models, there remains a significant gap between existing research and the needs of the industrial community. Contemporary manufacturing processes are inherently more complex - they may involve multiple stages of production or require the assessment of multiple quality characteristics. New and emerging fields, such as nanoelectronics and molecular biometrics, demand increased degrees of precision and estimation, that which is not attainable with current tools and measures. And since most researchers will focus on a specific type of characteristic or a given set of conditions, there are many critical industrial processes for which models are not applicable. Thus, the objective of this research is to improve existing techniques by not only expanding their range of applicability, but also their ability to more realistically model a given process. Several quality models are proposed that seek greater precision in the estimation of the process parameters and the removal of assumptions that limit their breadth and scope. An extension is made to examine the effectiveness of these models in both non-standard conditions and in areas that have not been previously investigated. Upon the completion of an in-depth literature review, various quality models are proposed, and numerical examples are used to validate the use of these methodologies