Physical Sciences and Mathematics Commons^™

Formulating An Efficient Statistical Test Using The Goodness Of Fit Approach With Applications To Real-Life Data, S. A. Qaid, S. E. Abo Youssef Prof., Mahmoud Mansour

Basic Science Engineering

Statistical tests are very important for researchers to make decisions. In particular, when the tests are non-parametric, they are of greater importance because they can be applied to a wide range of data sets regardless of knowing the distribution of these data. Researchers are therefore racing to obtain efficient tests for making good decisions based on the results of these tests. In this study, NBU (2)L was used based on the goodness of fit approach to present an efficient statistical test. The efficiency of the proposed test was computed, and the results were compared to those of other tests. Critical …

On Characterization Of The Exponential Distribution Via Hypoexponential Distributions, George Yanev

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

The sum of independent, but not necessary identically distributed, exponential random variables follows a hypoexponential distribution. We focus on a particular case when all but one rate parameters of the exponential variables are identical. This is known as exponentially modified Erlang distribution in molecular biology. We prove a characterization of the exponential distribution, which complements previous characterizations via hypoexponential distribution with all rates different from each other.

On Arnold–Villasenor Conjectures For Characterizaing Exponential Distribution Based On Sample Of Size Three, George Yanev

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

Arnold and Villasenor [4] obtain a series of characterizations of the exponential distribution based on random samples of size two. These results were already applied in constructing goodness-of-fit tests. Extending the techniques from [4], we prove some of Arnold and Villasenor’s conjectures for samples of size three. An example with simulated data is discussed.

Estimation Of The Burr Xii-Exponential Distribution Parameters, Gholamhossein Yari, Zahra Tondpour

Applications and Applied Mathematics: An International Journal (AAM)

The Burr XII distribution is one of the most important distributions in Survival analysis. In this article, we introduce the new wider Burr XII-G family of distributions. A special model in the new family called Burr XII-exponential distribution that has constant, decreasing and unimodal hazard rate functions is investigated. We discuss the estimation of this distribution parameters by maximum likelihood, three modifications of maximum likelihood and Bayes methods. In Bayes method, we use the uniform, triangular and Burr XII-uniform priors for posterior analysis and obtain Bayes estimations under two different loss functions. We obtain two approximations of the Bayes estimations, …

Exponentiated Weibull-Exponential Distribution With Applications, M. Elgarhy, M. Shakil, B. M. Golam Kibria

Applications and Applied Mathematics: An International Journal (AAM)

In this article, a new four-parameter continuous model, called the exponentiated Weibull exponential distribution, is introduced based on exponentiated Weibull-G family (Hassan and Elgarhy, 2016). The new model contains some new distributions as well as some former distributions. Various mathematical properties of this distribution are studied. General explicit expressions for the quantile function, expansion of distribution and density functions, moments, generating function, Rényi and q – entropies, and order statistics are obtained. The estimation of the model parameters is discussed using maximum likelihood method. The practical importance of the new distribution is demonstrated through real data set where we compare …

An Extended Weighted Exponential Distribution, Abbas Mahdavi, Leila Jabari

Journal of Modern Applied Statistical Methods

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.

Estimating The Parameter Of Exponential Distribution Under Type Ii Censoring From Fuzzy Data, Iman Makhdoom, Parviz Nasiri, Abbas Pak

Journal of Modern Applied Statistical Methods

The problem of estimating the parameter of Exponential distribution on the basis of type II censoring scheme is considered when the available data are in the form of fuzzy numbers. The Bayes estimate of the unknown parameter is obtained by using the approximation forms of Lindley (1980) and Tierney and Kadane (1986) under the assumption of gamma prior. The highest posterior density (HPD) estimate of the parameter of interest is found. A Monte Carlo simulation is used to compare the performances of the different methods. A real data set is investigated to illustrate the applicability of …

Power Comparison Of Some Goodness-Of-Fit Tests, Tianyi Liu

FIU Electronic Theses and Dissertations

There are some existing commonly used goodness-of-fit tests, such as the Kolmogorov-Smirnov test, the Cramer-Von Mises test, and the Anderson-Darling test. In addition, a new goodness-of-fit test named G test was proposed by Chen and Ye (2009). The purpose of this thesis is to compare the performance of some goodness-of-fit tests by comparing their power.

A goodness-of-fit test is usually used when judging whether or not the underlying population distribution differs from a specific distribution. This research focus on testing whether the underlying population distribution is an exponential distribution.

To conduct statistical simulation, SAS/IML is used in this research. Some …

Estimation Of The Parameters Of Exponential Distribution Using Top-K-Lists, M. Ahsanullah, Mohamed Habibullah

Applications and Applied Mathematics: An International Journal (AAM)

This paper deals with the estimation of location and scale parameters of the exponential distribution based on top-k-list of a sequence of observations from a two parameter exponential distribution. The minimum variance unbiased estimates of the location and scale parameters are given. Some comparisons of the variances of these estimates with respect to that of the kth record values are given.

Estimation Of Multi Component Systems Reliability In Stress-Strength Models, Adil H. Khan, T R. Jan

Journal of Modern Applied Statistical Methods

In a system with standby redundancy, there are a number of components only one of which works at a time and the other remain as standbys. When an impact of stress exceeds the strength of the active component, for the first time, it fails and another from standbys, if there is any, is activated and faces the impact of stresses, not necessarily identical as faced by the preceding component and the system fails when all the components have failed. Sriwastav and Kakaty (1981) assumed that the components stress-strengths are similarly distributed. However, in general the stress distributions will …

Distributional Properties Of Record Values Of The Ratio Of Independent Exponential And Gamma Random Variables, M. Shakil, M. Ahsanullah

Applications and Applied Mathematics: An International Journal (AAM)

Both exponential and gamma distributions play pivotal roles in the study of records because of their wide applicability in the modeling and analysis of life time data in various fields of applied sciences. In this paper, a distribution of record values of the ratio of independent exponential and gamma random variables is presented. The expressions for the cumulative distribution functions, moments, hazard function and Shannon entropy have been derived. The maximum likelihood, method of moments and minimum variance linear unbiased estimators of the parameters, using record values and the expressions to calculate the best linear unbiased predictor of record values, …

Generating Survival Times To Simulate Cox Proportional Hazards Models With Time-Varying Covariates., Peter C. Austin

Peter Austin

Simulations and Monte Carlo methods serve an important role in modern statistical research. They allow for an examination of the performance of statistical procedures in settings in which analytic and mathematical derivations may not be feasible. A key element in any statistical simulation is the existence of an appropriate data-generating process: one must be able to simulate data from a specified statistical model. We describe data-generating processes for the Cox proportional hazards model with time-varying covariates when event times follow an exponential, Weibull, or Gompertz distribution. We consider three types of time-varying covariates: first, a dichotomous time-varying covariate that can …

Adjusted Confidence Interval For The Population Median Of The Exponential Distribution, Moustafa Omar Ahmed Abu-Shawiesh

Journal of Modern Applied Statistical Methods

The median confidence interval is useful for one parameter families, such as the exponential distribution, and it may not need to be adjusted if censored observations are present. In this article, two estimators for the median of the exponential distribution, MD, are considered and compared based on the sample median and the maximum likelihood method. The first estimator is the sample median, MD₁, and the second estimator is the maximum likelihood estimator of the median, MD_MLE. Both estimators are used to propose a modified confidence interval for the population median of the exponential distribution, MD …

Estimating The Difference Of Percentiles From Two Independent Populations., Romual Eloge Tchouta

Electronic Theses and Dissertations

We first consider confidence intervals for a normal percentile, an exponential percentile and a uniform percentile. Then we develop confidence intervals for a difference of percentiles from two independent normal populations, two independent exponential populations and two independent uniform populations. In our study, we mainly focus on the maximum likelihood to develop our confidence intervals. The efficiency of this method is examined via coverage rates obtained in a simulation study done with the statistical software R.

Analysis Of Type-Ii Progressively Hybrid Censored Competing Risks Data, Debasis Kundu, Avijit Joarder

Journal of Modern Applied Statistical Methods

A Type-II progressively hybrid censoring scheme for competing risks data is introduced, where the experiment terminates at a pre-specified time. The likelihood inference of the unknown parameters is derived under the assumptions that the lifetime distributions of the different causes are independent and exponentially distributed. The maximum likelihood estimators of the unknown parameters are obtained in exact forms. Asymptotic confidence intervals and two bootstrap confidence intervals are also proposed. Bayes estimates and credible intervals of the unknown parameters are obtained under the assumption of gamma priors on the unknown parameters. Different methods have been compared using Monte Carlo simulations. One …

Statistical Reliability With Applications, Paul H. Kvam, Jye-Chyi Lu

Department of Math & Statistics Faculty Publications

This chapter reviews fundamental ideas in reliability theory and inference. The first part of the chapter accounts for lifetime distributions that are used in engineering reliability analyis, including general properties of reliability distributions that pertain to lifetime for manufactured products. Certain distributions are formulated on the basis of simple physical properties, and other are more or less empirical. The first part of the chapter ends with a description of graphical and analytical methods to find appropriate lifetime distributions for a set of failure data.

The second part of the chapter describes statistical methods for analyzing reliability data, including maximum likelihood …

Inference For P(Y, Vee Ming Ng

Journal of Modern Applied Statistical Methods

Some tests and confidence bounds for the reliability parameter R=P(Y

On The Linear Combination Of Exponential And Gamma Random Variables, Saralees Nadarajah, Samuel Kotz

Department of Statistics: Faculty Publications

The exact distribution of the linear combination αX + βY is derived when X and Y are exponential and gamma random variables distributed independently of each other. A measure of entropy of the linear combination is investigated. We also provide computer programs for generating tabulations of the percentage points associated with the linear combination. The work is motivated by examples in automation, control, fuzzy sets, neurocomputing and other areas of computer science.

Confidence Intervals For P(X Less Than Y) In The Exponential Case With Common Location Parameter, Ayman Baklizi

Journal of Modern Applied Statistical Methods

The problem considered is interval estimation of the stress - strength reliability R = P(Xθ and λ respectively and a common location parameter μ . Several types of asymptotic, approximate and bootstrap intervals are investigated. Performances are investigated using simulation techniques and compared in terms of attainment of the nominal confidence level, symmetry of lower and upper error rates, and expected length. Recommendations concerning their usage are given.

Step-Stress Testing In Agricultijre, Imad H. Khamis, James J. Higgins

Conference on Applied Statistics in Agriculture

Step-stress testing has been used for a munber years in engineering. An item is placed on test for a specified period of time. If it does not fail in that time, the stress is increased. This process is repeated for a specified number of stress levels until the item fails. In agriculture, animals or plants may be the test items and dosage of a chemical, amount of fertilizer, temperature, etc, the stress variable. In this paper we suggest several potential applications of step-stress testing in agriculture and present inferential procedures for observations that are distributed exponentially.

Prediction Intervals, Based On Ranges And Waiting Times, For An Exponential Distribution, Laura Colangelo, Jagdish K. Patel

Mathematics and Statistics Faculty Research & Creative Works

This article contains two prediction intervals applicable to a 2-parameter as well as a 1-parameter exponential distribution. One can be used to predict a future sample range on the basis of an observed sample range. Appropriate prediction factors are tabulated. The other can be used to predict a waiting time between two future successive failures on the basis of an observed waiting time between two previous successive failures. © 1992 IEEE