Power Lindley distribution and associated inference
TL;DR: A new two-parameter power Lindley distribution is introduced and its properties are discussed, which include the shapes of the density and hazard rate functions, the moments, skewness and kurtosis measures, the quantile function, and the limiting distributions of order statistics.
About: This article is published in Computational Statistics & Data Analysis.The article was published on 2013-08-01. It has received 269 citations till now. The article focuses on the topics: Likelihood function & Normal distribution.
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TL;DR: An extensive review of some discrete and continuous versions of the modifications of the Weibull distribution to allow for non-monotonic hazard functions.
156 citations
Book•
17 Jul 2015
TL;DR: This book is suitable for undergraduate students attending master programs from applied mathematics and mathematical modelling and readers with some computational programming skills may find numerous ideas for writing their own programs to run graphics of various sigmoid functions.
Abstract: The subject of this book is cross-disciplinary. Sigmoid functions present a field of interest both for fundamental as well as application-driven research. We have tried to give the readers the flavour of both perspectives. From the perspective of fundamental science sigmoid functions are of special interest in abstract areas such as approximation theory and probability theory. More specifically, sigmoid function are an object of interest in Hausdorff approximations, fuzzy set theory, cumulative distribution functions, etc. From the perspective of applied mathematics and modelling sigmoid functions find their place in numerous areas of life and social sciences, physics and engineering, to mention a few familiar applications: population dynamics, artificial neural networks, signal and image processing. We consider this book to be suitable for undergraduate students attending master programs from applied mathematics and mathematical modelling. Readers with some computational programming skills may find numerous ideas for writing their own programs to run graphics of various sigmoid functions (the ones presented in the book make use of the computer algebra system Mathematica).
85 citations
Cites methods from "Power Lindley distribution and asso..."
...[93] The exponentiated power Lindley function with three parameters is defined by:...
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...[93] The exponentiated power Lindley function with 2 parameters is defined by:...
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01 Jan 2015
TL;DR: In this paper, a new one parameter lifetime distribution named "Akash distribution" for modeling lifetime data has been introduced, which has been discussed using maximum likelihood estimation and method of moments, the usefulness and applicability of the proposed distribution have been discussed and illustrated with two real lifetime data sets from medical science and engineering.
Abstract: A new one parameter lifetime distribution named "Akash distribution" for modeling lifetime data has been introduced. Some important mathematical properties of the proposed distribution including its shape, moments, skewness, kurtosis, hazard rate function, mean residual life function, stochastic ordering, mean deviations, order statistics, Bonferroni and Lorenz curves, Renyi entropy measure, stress-strength reliability have been discussed. The condition under which Akash distribution is over-dispersed, equi-dispersed, and under-dispersed are presented along with the conditions under which exponential and Lindley distributions are over-dispersed, equi-dispersed and under-dispersed. The estimation of its parameter has been discussed using maximum likelihood estimation and method of moments. The usefulness and the applicability of the proposed distribution have been discussed and illustrated with two real lifetime data sets from medical science and engineering.
78 citations
TL;DR: A three-parameters continuous distribution, namely, Power Lomax distribution (POLO) is proposed and studied for remission times of bladder cancer data and the characteristics of the fitting data using the proposed distribution are compared with known extensions of LomAX distribution.
Abstract: A three-parameters continuous distribution, namely, Power Lomax distribution (POLO) is proposed and studied for remission times of bladder cancer data. POLO distribution accommodate both inverted bathtub and decreasing hazard rate. Several statistical and reliability properties are derived. Point estimation via method of moments and maximum likelihood and the interval estimation are also studied. The simulation schemes are calculated to examine the bias and mean square error of the maximum likelihood parameter estimators. Finally, a real data application about the remission time of bladder cancer is used to illustrate the usefulness of the proposed distribution in modelling real data application. The characteristics of the fitting data using the proposed distribution are compared with known extensions of Lomax distribution. The comparison showed that the POLO distribution outfit most well-known extensions of Lomax distribution.
75 citations
TL;DR: The point and interval estimation of R, based on maximum likelihood, nonparametric and parametric bootstrap methods, are developed and the performance of the point estimate and confidence interval of R under the considered estimation methods is studied through extensive simulation.
Abstract: In this paper, we are interested in the estimation of the reliability parameter R = P(X > Y) where X, a component strength, and Y, a component stress, are independent power Lindley random variables. The point and interval estimation of R, based on maximum likelihood, nonparametric and parametric bootstrap methods, are developed. The performance of the point estimate and confidence interval of R under the considered estimation methods is studied through extensive simulation. A numerical example, based on a real data, is presented to illustrate the proposed procedure.
72 citations
Cites background from "Power Lindley distribution and asso..."
...…to Prof. M. E. Ghitany, PhD, Department of Statistics and Operations Research, Faculty of Science, Kuwait University, Safat 13060, Kuwait; E-mail: meghitany@ yahoo.com 118 Ghitany et al. (2013) introduced a new extension of the Lindley distribution by considering the power transformation X = V 1/α....
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References
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Book•
01 Jan 1943TL;DR: Combinations involving trigonometric and hyperbolic functions and power 5 Indefinite Integrals of Special Functions 6 Definite Integral Integral Functions 7.Associated Legendre Functions 8 Special Functions 9 Hypergeometric Functions 10 Vector Field Theory 11 Algebraic Inequalities 12 Integral Inequality 13 Matrices and related results 14 Determinants 15 Norms 16 Ordinary differential equations 17 Fourier, Laplace, and Mellin Transforms 18 The z-transform
Abstract: 0 Introduction 1 Elementary Functions 2 Indefinite Integrals of Elementary Functions 3 Definite Integrals of Elementary Functions 4.Combinations involving trigonometric and hyperbolic functions and power 5 Indefinite Integrals of Special Functions 6 Definite Integrals of Special Functions 7.Associated Legendre Functions 8 Special Functions 9 Hypergeometric Functions 10 Vector Field Theory 11 Algebraic Inequalities 12 Integral Inequalities 13 Matrices and related results 14 Determinants 15 Norms 16 Ordinary differential equations 17 Fourier, Laplace, and Mellin Transforms 18 The z-transform
27,354 citations
6,036 citations
Book•
01 Jan 1950
TL;DR: In this paper, the authors present an approach for estimating the average risk of a risk-optimal risk maximization algorithm for a set of risk-maximization objectives, including maximalaxity and admissibility.
Abstract: Preface to the Second Edition.- Preface to the First Edition.- List of Tables.- List of Figures.- List of Examples.- Table of Notation.- Preparations.- Unbiasedness.- Equivariance.- Average Risk Optimality.- Minimaxity and Admissibility.- Asymptotic Optimality.- References.- Author Index.- Subject Index.
4,382 citations
Book•
01 Jul 1992TL;DR: In this paper, the authors use order statistics in Statistical Inference Asymptotic Theory Record Values Bibliography Indexes to measure moment relations, bounds, and approximations.
Abstract: Basic Distribution Theory Discrete Order Statistics Order Statistics from Some Specific Distributions Moment Relations, Bounds, and Approximations Characterizations Using Order Statistics Order Statistics in Statistical Inference Asymptotic Theory Record Values Bibliography Indexes.
1,605 citations
"Power Lindley distribution and asso..." refers background in this paper
...(8.4.2) and (8.4.3) of Arnold et al. (1992)....
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...Therefore, by Theorem 8.3.3 of Arnold et al. (1992), the maximal domain of attraction of the PL(α, β) distribution is the standard Gumbel distribution, proving Part (b)....
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...6(ii) of Arnold et al. (1992), the minimal domain of attraction of the PL(α, β) distribution is the standard Weibull distribution, proving Part (a)....
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...Therefore, by Theorem 8.3.6(ii) of Arnold et al. (1992), the minimal domain of attraction of the PL(α, β) distribution is the standard Weibull distribution, proving Part (a)....
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...3 of Arnold et al. (1992), the maximal domain of attraction of the PL(α, β) distribution is the standard Gumbel distribution, proving Part (b)....
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