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Muhammad Shuaib Khan - One of the best experts on this subject based on the ideXlab platform.
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Transmuted Modified Inverse Weibull Distribution: Properties and application
Pakistan Journal of Statistics and Operation Research, 2019Co-Authors: Muhammad Shuaib KhanAbstract:This paper examines the potential usefulness of the transmuted modified inverse Weibull Distribution. This four-parameter Distribution holds eleven life time Distributions as special cases. Theoretical properties of the transmuted modified inverse Weibull Distribution are studied; which includes the quantile, median, entropy, mean deviations, mean, geometric mean and harmonic mean. The estimation of parameters is obtained by using the method of maximumlikelihood. An application to real dataset is provided to show the better fit of the transmuted modified inverse Weibull Distribution.
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Transmuted Weibull Distribution: Properties and estimation
Communications in Statistics - Theory and Methods, 2016Co-Authors: Muhammad Shuaib Khan, Robert King, Irene L. HudsonAbstract:In this article, we investigate the potential usefulness of the three-parameter transmuted Weibull Distribution for modeling survival data. The main advantage of this Distribution is that it has increasing, decreasing or constant instantaneous failure rate depending on the shape parameter and the new transmuting parameter. We obtain several mathematical properties of the transmuted Weibull Distribution such as the expressions for the quantile function, moments, geometric mean, harmonic mean, Shannon, Renyi and q-entropies, mean deviations, Bonferroni and Lorenz curves, and the moments of order statistics. We propose a location-scale regression model based on the log-transmuted Weibull Distribution for modeling lifetime data. Applications to two real datasets are given to illustrate the flexibility and potentiality of the transmuted Weibull family of lifetime Distributions.
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transmuted modified Weibull Distribution a generalization of the modified Weibull probability Distribution
European Journal of Pure and Applied Mathematics, 2013Co-Authors: Muhammad Shuaib Khan, Robert KingAbstract:T his paper introduces a transmuted modified Weibull Distribution as an important compet- itive model which contains eleven life time Distributions as special cases. We generalized the three parameter modified Weibull Distribution using the quadratic rank transmutation map studied by Shaw et al. (12) to develop a transmuted modified Weibull Distribution. The properties of the transmuted modified Weibull Distribution are discussed. Least square estimation is used to evaluate the parame- ters. Explicit expressions are derived for the quantiles. We derive the moments and examine the order statistics. We propose the method of maximum likelihood for estimating the model parameters and obtain the observed information matrix. This model is capable of modeling of various shapes of aging and failure criteria. 2010 Mathematics Subject Classifications: 90B25; 62N05
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Modified Inverse Weibull Distribution
Journal of Statistics Applications & Probability, 2012Co-Authors: Muhammad Shuaib Khan, Robert KingAbstract:A generalized version of four parameter modified inverse Weibull Distribution (MIWD) is introduced in this paper. This Distribution generalizes the following Distributions: (1) Modified Inverse exponential Distribution, (2) Modified Inverse Rayleigh Distribution, (3) Inverse Weibull Distribution. We provide a comprehensive description of the mathematical properties of the modified inverse Weibull Distribution along with its reliability behaviour. We derive the moments, moment generating function and examine the order statistics. We propose the method of maximum likelihood for estimating the model parameters and obtain the observed information matrix. The inverse Weibull Distribution is the life time probability Distribution which is used in the reliability engineering discipline. The inverse Weibull Distribution can be used to model a variety of failure characteristics such as infant mortality, useful life and wear-out periods. Reliability and failure data both from life testing and in service records which is often modeled by the life time Distributions such as the inverse exponential, inverse Rayleigh, inverse Weibull Distributions. In this research we have developed a new reliability model called modified inverse Weibull Distribution. This paper focuses on all the properties of this model and presents the graphical analysis of modified inverse Weibull reliability models. This paper present the relationship between shape parameter and other properties such as non- reliability function, reliability function, instantaneous failure rate, cumulative instantaneous failure rate models. This life time Distribution is capable of modeling of various shapes of aging and failure criteria.The proposed model can be used as an alternative to inverse generalized exponential, inverse generalized Rayleigh, inverse generalized Weibull Distributions. The cumulative Distribution function (CDF) of the Inverse Weibull Distribution is denoted by
Ilhan Usta - One of the best experts on this subject based on the ideXlab platform.
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analysis of the upper truncated Weibull Distribution for wind speed
Energy Conversion and Management, 2015Co-Authors: Yeliz Mert Kantar, Ilhan UstaAbstract:Accurately modeling wind speed is critical in estimating the wind energy potential of a certain region. In order to model wind speed data smoothly, several statistical Distributions have been studied. Truncated Distributions are defined as a conditional Distribution that results from restricting the domain of statistical Distribution and they also cover base Distribution. This paper proposes, for the first time, the use of upper-truncated Weibull Distribution, in modeling wind speed data and also in estimating wind power density. In addition, a comparison is made between upper-truncated Weibull Distribution and well known Weibull Distribution using wind speed data measured in various regions of Turkey. The obtained results indicate that upper-truncated Weibull Distribution shows better performance than Weibull Distribution in estimating wind speed Distribution and wind power. Therefore, upper-truncated Weibull Distribution can be an alternative for use in the assessment of wind energy potential.
Robert King - One of the best experts on this subject based on the ideXlab platform.
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Transmuted Weibull Distribution: Properties and estimation
Communications in Statistics - Theory and Methods, 2016Co-Authors: Muhammad Shuaib Khan, Robert King, Irene L. HudsonAbstract:In this article, we investigate the potential usefulness of the three-parameter transmuted Weibull Distribution for modeling survival data. The main advantage of this Distribution is that it has increasing, decreasing or constant instantaneous failure rate depending on the shape parameter and the new transmuting parameter. We obtain several mathematical properties of the transmuted Weibull Distribution such as the expressions for the quantile function, moments, geometric mean, harmonic mean, Shannon, Renyi and q-entropies, mean deviations, Bonferroni and Lorenz curves, and the moments of order statistics. We propose a location-scale regression model based on the log-transmuted Weibull Distribution for modeling lifetime data. Applications to two real datasets are given to illustrate the flexibility and potentiality of the transmuted Weibull family of lifetime Distributions.
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Characterisations of the transmuted inverse Weibull Distribution
Anziam Journal, 2014Co-Authors: M. Shuaib Khan, Robert King, Irene L. HudsonAbstract:We characterise the transmuted inverse Weibull Distribution and compare it to many other generalizations of the two-parameter inverse Weibull Distribution using the likelihood ratio test. Explicit expressions are derived for the quantile, moment generating function, entropies, mean deviation and order statistics. A bladder cancer application is presented to illustrate the proposed transmuted inverse Weibull Distribution.
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transmuted modified Weibull Distribution a generalization of the modified Weibull probability Distribution
European Journal of Pure and Applied Mathematics, 2013Co-Authors: Muhammad Shuaib Khan, Robert KingAbstract:T his paper introduces a transmuted modified Weibull Distribution as an important compet- itive model which contains eleven life time Distributions as special cases. We generalized the three parameter modified Weibull Distribution using the quadratic rank transmutation map studied by Shaw et al. (12) to develop a transmuted modified Weibull Distribution. The properties of the transmuted modified Weibull Distribution are discussed. Least square estimation is used to evaluate the parame- ters. Explicit expressions are derived for the quantiles. We derive the moments and examine the order statistics. We propose the method of maximum likelihood for estimating the model parameters and obtain the observed information matrix. This model is capable of modeling of various shapes of aging and failure criteria. 2010 Mathematics Subject Classifications: 90B25; 62N05
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Modified Inverse Weibull Distribution
Journal of Statistics Applications & Probability, 2012Co-Authors: Muhammad Shuaib Khan, Robert KingAbstract:A generalized version of four parameter modified inverse Weibull Distribution (MIWD) is introduced in this paper. This Distribution generalizes the following Distributions: (1) Modified Inverse exponential Distribution, (2) Modified Inverse Rayleigh Distribution, (3) Inverse Weibull Distribution. We provide a comprehensive description of the mathematical properties of the modified inverse Weibull Distribution along with its reliability behaviour. We derive the moments, moment generating function and examine the order statistics. We propose the method of maximum likelihood for estimating the model parameters and obtain the observed information matrix. The inverse Weibull Distribution is the life time probability Distribution which is used in the reliability engineering discipline. The inverse Weibull Distribution can be used to model a variety of failure characteristics such as infant mortality, useful life and wear-out periods. Reliability and failure data both from life testing and in service records which is often modeled by the life time Distributions such as the inverse exponential, inverse Rayleigh, inverse Weibull Distributions. In this research we have developed a new reliability model called modified inverse Weibull Distribution. This paper focuses on all the properties of this model and presents the graphical analysis of modified inverse Weibull reliability models. This paper present the relationship between shape parameter and other properties such as non- reliability function, reliability function, instantaneous failure rate, cumulative instantaneous failure rate models. This life time Distribution is capable of modeling of various shapes of aging and failure criteria.The proposed model can be used as an alternative to inverse generalized exponential, inverse generalized Rayleigh, inverse generalized Weibull Distributions. The cumulative Distribution function (CDF) of the Inverse Weibull Distribution is denoted by
Yeliz Mert Kantar - One of the best experts on this subject based on the ideXlab platform.
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analysis of the upper truncated Weibull Distribution for wind speed
Energy Conversion and Management, 2015Co-Authors: Yeliz Mert Kantar, Ilhan UstaAbstract:Accurately modeling wind speed is critical in estimating the wind energy potential of a certain region. In order to model wind speed data smoothly, several statistical Distributions have been studied. Truncated Distributions are defined as a conditional Distribution that results from restricting the domain of statistical Distribution and they also cover base Distribution. This paper proposes, for the first time, the use of upper-truncated Weibull Distribution, in modeling wind speed data and also in estimating wind power density. In addition, a comparison is made between upper-truncated Weibull Distribution and well known Weibull Distribution using wind speed data measured in various regions of Turkey. The obtained results indicate that upper-truncated Weibull Distribution shows better performance than Weibull Distribution in estimating wind speed Distribution and wind power. Therefore, upper-truncated Weibull Distribution can be an alternative for use in the assessment of wind energy potential.
Saad J. Almalki - One of the best experts on this subject based on the ideXlab platform.
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Modifications of the Weibull Distribution: A review
Reliability Engineering & System Safety, 2014Co-Authors: Saad J. Almalki, Saralees NadarajahAbstract:It is well known that the Weibull Distribution is the most popular and the most widely used Distribution in reliability and in analysis of lifetime data. Unfortunately, its hazard function cannot exhibit non-monotonic shapes like the bathtub shape or the unimodal shape. Since 1958, the Weibull Distribution has been modified by many researchers to allow for non-monotonic hazard functions. This paper gives an extensive review of some discrete and continuous versions of the modifications of the Weibull Distribution.
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A new modified Weibull Distribution
Reliability Engineering & System Safety, 2013Co-Authors: Saad J. Almalki, Jingsong YuanAbstract:We introduce a new lifetime Distribution by considering a serial system with one component following a Weibull Distribution and another following a modified Weibull Distribution. We study its mathematical properties including moments and order statistics. The estimation of parameters by maximum likelihood is discussed. We demonstrate that the proposed Distribution fits two well-known data sets better than other modified Weibull Distributions including the latest beta modified Weibull Distribution. The model can be simplified by fixing one of the parameters and it still provides a better fit than existing models.
