The associated PDF of (3) has the formwhere is the baseline PDF. For k = 1, the density function tends to 1/λ as x approaches zero from above and is strictly decreasing. This paper proposes the new three-parameter type I half-logistic inverse Weibull (TIHLIW) distribution which generalizes the inverse Weibull model. Mean Residual Life and Mean Waiting Time. The inverse Weibull (IW) distribution is also known as reciprocal Weibull distribution (see [1, 2]). Journal of Statistics Applications & Probability. Finally, the application of the proposed new distribution to a real data representing the waiting time before customer service in the bank is given and its goodness-of-fit is demonstrated. In this paper, we propose a new lifetime model called the, type I half-logistic inverse Weibull (TIHLIW) model. For k = 1 the density has a finite negative slope at x = 0. This class is found to be capable of modeling lifetime and other application data. A three-parameter generalized inverse Weibull distribution with decreasing and unimodal failure rate is introduced The inverse Weibull distribution has the ability to model failure rates which are quite common in reliability and biological studies. A new e density function of the TIHLIW can be expressed as a linear combination of the inverse Weibull, densities. Using the PDF and CDF of the TIHLIW distribution. Many generalized classes of distributions have been proposed for modeling real-life data in several applied fields such as reliability, engineering, biological studies, economics, medical sciences, environmental sciences, and finance. , Springer Science and Business Media, Berlin, Journal of Statistical Computation and Simulation, Wahrs cheinlichkeit , Statistik und Wahrheit. probability weighted moments and characterizations are obtained. [31], exponentiated transmuted, generalized Rayleigh (ETGR) by Afify et al. [7] M. Pararai, G. Warahena-Liyanage, and B. O. new class of generalized inverse Weibull distribution with, Weibull and related distributions with applications,”, tronic Journal of Applied Statistical Analysis, Weibull distribution: eory and application,”, A. M. Basheer, “Extended inverse Weibull distribution with, [11] A. M. Basheer, “Alpha power inverse Weibull distribution, [12] A. Marshall and I. Olkin, “A new method for adding a pa-, rameter to a family of distributions with application to the, distributions: Beyond Gram-Charlier expansions and a Skew-, Kurtotic-Normal distribution from a rank transmutation. estimation procedures, namely; maximum likelihood, percentiles and least squares, are used. ScienceDirect ® is a registered trademark of Elsevier B.V. ScienceDirect ® is a registered trademark of Elsevier B.V. Extended inverse Weibull distribution with reliability application. Quantile and Moment-Generating Functions. Some of its mathematical properties including explicit expressions for The corresponding PDF of (4) reduces to Some explicit, expressions for mathematical quantities of the TIHLIW, distribution are derived. I am working on constructing some new families of probability distributions. is paper proposes the new three-parameter type I half-logistic inverse Weibull (TIHLIW) distribution which generalizes the, inverse Weibull model. The usefulness of the new distribution is illustrated in real, Providing extended and generalized distribution is usually precious for many statisticians. The hazard rate function (HRF) of the TIHL-G family is This class is a generalization of the two-parameter Weibull distribution as well as some other lifetime distributions. Four estimation methods, namely, the maximum likelihood, least squares, weighted least squares, and Cramér–von Mises methods, are utilized to estimate the TIHLIW parameters. Some of its structural properties are obtained such as the ordinary and incomplete moments, quantile and generating functions, order statistics and probability weighted moments. 1. [24] and Cordeiro et al. Some mathematical quantities of the proposed TIHLIW model are derived. ese data. In addition, the estimation of the stress-strength parameter is discussed. The maximum likelihood method is used for estimating the model parameters, and the finite sample performance of the estimators is assessed by simulation. Kumaraswamy modified IW by Aryal and Elbatal [9], Marshall-Olkin IW by Okasha et al. Introduction the new distribution compared with some known distributions. For k > 1, the density function tends to zero as x approaches zero from above, increases until its mode and decreases after it. The estimation of the model parameters is performed by maximum likelihood method. Simulation results are presented to assess the performance of the proposed estimation methods. All figure content in this area was uploaded by Ahmed Z. Afify, All content in this area was uploaded by Ahmed Z. Afify on Oct 21, 2020, The Extended Inverse Weibull Distribution: Properties, Department of Quantitative Analysis, King Saud University, Riyadh, Saudi Arabia, Department of Statistics, Mathematics and Insurance, BenhaUniversity, Banha, Egypt. close fits to relief times data than other fitted models. 4.2. Keller et al. Let, from the TIHLIW distribution, and then the LSEs and, Further, the LSEs and WLSEs of the TIHLIW parameters, are also obtained by solving the following nonlinear equa-, (CVM) method [21, 22], the CVMEs of the TIHLIW pa-, rameters can be constructed by minimizing, obtained by solving the following nonlinear equations si-, In this section, we conduct a simulation study to compare, the performance of the different estimators based on the, mean square error criterion. The density function of the TIHLIW can be expressed as a linear combination of the inverse Weibull densities. Here, we obtain the MGF of the IW dis-, Using the Wright generalized hypergeometric function, e MGF of the IW distribution has the form, e first incomplete moment which follows by setting. have been analyzed by Afify et al. Extended Lifetime Models and Their Applications, Institute of Statistical Studies and Research, Alpha power inverse Weibull distribution with reliability application, The odd Lomax generator of distributions: Properties, estimation and applications, The Extended Odd Weibull-G Family: Properties and Applications, An Extended Burr XII Distribution: Properties, Inference and Applications, The Odd Exponentiated Half-Logistic-G Family: Properties, Characterizations and Applications, The Beta Generalized Inverse Weibull Geometric Distribution, Extended inverse Weibull distribution with reliability application, The beta transmuted-H family for lifetime data, Kumaraswamy modified inverse Weibull distribution: Theory and application, Survival Distributions: Reliability Applications in the Biomedical Sciences, Some New Generated Families of Distributions with Applications, A weighted three-parameter Weibull distribution, The odd Frѐchet inverse Rayleigh distribution: statistical properties and applications, A NEW GENERALIZATION OF ERLANG-TRUNCATED EXPONENTIAL DISTRIBUTION: PROPERTIES AND APPLICATIONS, Odds Generalized Exponential-Inverse Weibull Distribution: Properties & Estimation.

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