International Journal of Statistics and Probability, 2020
A goal of this research is providing new probability distribution called Sinh inverted exponentia... more A goal of this research is providing new probability distribution called Sinh inverted exponential distribution. The new distribution was extensively depending on the hyperbolic sine family of distributions with exponential distribution as a baseline distribution. Valuable statistical properties of the proposed distribution including mathematical and asymptotic expressions for its probability density function and Reliability. Moments, quantiles, moment generating function, failure rate function, mean residual lifetime, order statistics and entropies are derived. Actually, the applicability and validation of this model is proved in simulation study and an application to neck cancer disease data.
The Journal of Advanced Research in Applied Mathematics, 2019
We introduce a new lifetime distribution with six parameters. This distribution is called the add... more We introduce a new lifetime distribution with six parameters. This distribution is called the additive Weibull log logistic (AWLL) distribution based on the additive Weibull-generated family of distributions and the log logistic distribution as a baseline distribution. Important linear expansion forms for the cdf, pdf and reliability are obtained. Some statistical properties of the AWLL distribution including moments, incomplete moments, mean deviation, mode, median, skewness, and kurtosis are studied. Explicit expressions for the quantile function, moment-generating function and order statistics are obtained. The estimation of model parameters is discussed, using maximum likelihood method and the simulation study is conducted. The importance of the AWLL distribution is demonstrated through real data set compared with several lifetime distributions.
A new family of inverse probability distributions named inverse Rayleigh family is introduced to ... more A new family of inverse probability distributions named inverse Rayleigh family is introduced to generate many continuous distributions. The shapes of probability density and hazard rate functions are investigated. Some Statistical measures of the new generator including moments, quantile and generating functions, entropy measures and order statistics are derived. The Estimation of the model parameters is performed by the maximum likelihood estimation method. Furthermore, a simulation study is used to estimate the parameters of one of the members of the new family. The data application shows that the new family models can be useful to provide better fits than other lifetime models
Far East Journal of Mathematical Sciences (FJMS), 2019
This paper introduces a new generator for continuous distributions in three extra parameters. It ... more This paper introduces a new generator for continuous distributions in three extra parameters. It is called the generalized inverse Weibull generated (GIW-G) family of distributions. The paper also introduces selected special models of family and explicit expressions of the GIWG family. Important mathematical properties of the family are obtained, for example, quantile and generating functions, ordinary and incomplete moments, mean deviations and the expressions of order statistics. The parameter estimates of the family are calculated using the maximum likelihood method and the simulation study of a new model belonging to the GIW-G family is conducted. The efficiency and importance of the family have been tested through real data set.
International Journal of Statistics and Probability, 2020
A goal of this research is providing new probability distribution called Sinh inverted exponentia... more A goal of this research is providing new probability distribution called Sinh inverted exponential distribution. The new distribution was extensively depending on the hyperbolic sine family of distributions with exponential distribution as a baseline distribution. Valuable statistical properties of the proposed distribution including mathematical and asymptotic expressions for its probability density function and Reliability. Moments, quantiles, moment generating function, failure rate function, mean residual lifetime, order statistics and entropies are derived. Actually, the applicability and validation of this model is proved in simulation study and an application to neck cancer disease data.
In this article, a new four-parameter lifetime model named the Weibull quasi Lindley distribution... more In this article, a new four-parameter lifetime model named the Weibull quasi Lindley distribution based on the Weibull G-family is introduced. It is more flexible than several recently introduced lifetime distributions. Various structural properties of the new distribution are derived including moments, moment generating function, quantile function, reliability, hazard rate function and mean residual life. Expressions for the R´enyi, q-entropies and density function of order statistics are also obtained. The model parameters are estimated by the method of maximum likelihoodand the observed information matrix is determined. Two real data sets are presented to illustrate the advantage of the new distribution. In fact, the new model provides a better fit to this data than some of the most important distributions.
International Journal of Statistics and Probability, 2017
In this paper, we present a new family, depending on additive Weibull random variable as a genera... more In this paper, we present a new family, depending on additive Weibull random variable as a generator, called the generalized additive Weibull generated-family (GAW-G) of distributions with two extra parameters. The proposed family involves several of the most famous classical distributions as well as the new generalized Weibull-G family which already accomplished by Cordeiro et al. (2015). Four special models are displayed. The expressions for the incomplete and ordinary moments, quantile, order statistics, mean deviations, Lorenz and Benferroni curves are derived. Maximum likelihood method of estimation is employed to obtain the parameter estimates of the family. The simulation study of the new models is conducted. The efficiency and importance of the new generated family is examined through real data sets.
In this paper a new continuous distribution with extra two parameters called the Weibull exponent... more In this paper a new continuous distribution with extra two parameters called the Weibull exponentiated inverse Raleigh distribution is introduced. The new distribution based on the Weibull generated family of distributions and exponentiated inverse Raleigh distribution as a baseline distribution. Important linear expansion forms for the cdf, pdf and reliability are obtained. We investigate the shapes of the density and hazard rate function. Some statistical properties of the new distribution including moments, mean residual life, quantile and generating functions, median, skewness and kurtosis and order statistics are discussed. The estimation of the model parameters is performed by the maximum likelihood method. The importance of the new distribution is examined through real data application and the results show that the new distribution can be useful to provide better fits than other lifetime models.
The additive Weibull distribution is an extended version of the most widely used Weibull distribu... more The additive Weibull distribution is an extended version of the most widely used Weibull distribution which is a quite flexible model for analyzing lifetime data. In this paper, a new family of distributions called additive Weibull generated (AW-G) is defined and studied.The new family includes the Weibull-G family which was previously worked out by Bourguignon et al. [7]. Four sub-models are introduced and studied in some details. Explicit expressions for the ordinary moments, quantile, order statistics and reliability are obtained. The method of maximum likelihood is used to estimate the model parameters of the family. The additive Weibull-G family may serve as a viable alternative to other distributions for modeling data arising in various fields such as the physical and biological sciences, survival analysis and engineering. The importance of the additive Weibull-G family is concluded by means of two real data sets.
This research includes new probability distribution which is named beta inverted Lindley distribu... more This research includes new probability distribution which is named beta inverted Lindley distribution. Some useful functions of the proposed distribution are derived. Important mathematical expansions are investigated. Statistical measures including; quantiles, moments, incomplete moments, Renyi and s entropies are acquired. Extra statistical properties such as mean deviations, central of tendency measures, coefficient of variation, coefficients of skewness and kurtosis are defined. The Bonferroni and Lorenz curves are conducted and the stress- strength reliability is computed. The maximum likelihood method is used to estimate parameters of beta inverted Lindley distribution. The importance and significance of the introduced model are applied through failure times data set. The main aim behind generalization is to make more flexibility to the distribution so that more data can be analyzed using the new distribution. The model parameters are estimated using maximum likelihood estimat...
In this study, an extended exponentiated Pareto distribution is proposed. Some statistical proper... more In this study, an extended exponentiated Pareto distribution is proposed. Some statistical properties are derived. We consider maximum likelihood, least squares, weighted least squares and Bayesian estimators. A simulation study is implemented for investigating the accuracy of different estimators. An application of the proposed distribution to a real data is presented.
International Journal of Statistics and Probability, 2020
A goal of this research is providing new probability distribution called Sinh inverted exponentia... more A goal of this research is providing new probability distribution called Sinh inverted exponential distribution. The new distribution was extensively depending on the hyperbolic sine family of distributions with exponential distribution as a baseline distribution. Valuable statistical properties of the proposed distribution including mathematical and asymptotic expressions for its probability density function and Reliability. Moments, quantiles, moment generating function, failure rate function, mean residual lifetime, order statistics and entropies are derived. Actually, the applicability and validation of this model is proved in simulation study and an application to neck cancer disease data.
A new generalization of inverse Lindley distribution, called Kumaraswamy inverse Lindley is prese... more A new generalization of inverse Lindley distribution, called Kumaraswamy inverse Lindley is presented in this study. Some mathematical expressions are determined for the proposed distribution. Significant statistical measures are deduced including quantiles, generating functions, ordinary and incomplete moments, entropies, mean deviations, and order statistics. Some other properties like median, mean, variance, coefficient of variation, coefficients of skewness, and kurtosis are characterized. Moreover, stress-strength reliability is defined. A simulation study of the Kumaraswamy inverse distribution is introduced using maximum likelihood estimation and the performances of their estimates are compared through biases and mean square errors. The applicability and importance of the new distribution are illustrated through two real data sets. https://dx. Bu çalışmada, Kumaraswamy ters Lindley adı verilen ters Lindley dağılımının yeni bir genellemesi sunulmuştur. Önerilen dağılım için bazı matematiksel ifadeler belirlenmiştir. Nicelikler, üreten fonksiyonlar, sıradan ve eksik anlar, entropiler, ortalama sapmalar ve sıra istatistikleri dahil olmak üzere önemli istatistiksel ölçümler çıkarılmıştır. Medyan, ortalama, varyans, varyasyon katsayısı, çarpıklık katsayıları ve basıklık gibi diğer bazı özellikler karakterize edilmiştir. Dahası, gerilme mukavemeti güvenilirliği tanımlanmıştır. Kumaraswamy ters dağılımının bir simülasyon çalışması, maksimum olasılık tahmini kullanılarak tanıtılmış ve tahminlerinin performansları, önyargılar ve ortalama kare hataları ile karşılaştırılmıştır. Yeni dağıtımın uygulanabilirliği ve önemi iki gerçek veri seti ile gösterilmektedir. https://dx.
International Journal of Statistics and Probability, 2020
A goal of this research is providing new probability distribution called Sinh inverted exponentia... more A goal of this research is providing new probability distribution called Sinh inverted exponential distribution. The new distribution was extensively depending on the hyperbolic sine family of distributions with exponential distribution as a baseline distribution. Valuable statistical properties of the proposed distribution including mathematical and asymptotic expressions for its probability density function and Reliability. Moments, quantiles, moment generating function, failure rate function, mean residual lifetime, order statistics and entropies are derived. Actually, the applicability and validation of this model is proved in simulation study and an application to neck cancer disease data.
Far East Journal of Mathematical Sciences (FJMS) Volume 112, Issue 2, Pages 237 - 266 , 2019
This paper introduces a new generator for continuous distributions in three extra parameters. It ... more This paper introduces a new generator for continuous distributions in three extra parameters. It is called the generalized inverse Weibull generated (GIW-G) family of distributions. The paper also introduces selected special models of family and explicit expressions of the GIWG family. Important mathematical properties of the family are obtained, for example, quantile and generating functions, ordinary and incomplete moments, mean deviations and the expressions of order statistics. The parameter estimates of the family are calculated using the maximum likelihood method and the simulation study of a new model belonging to the GIW-G family is conducted. The efficiency and importance of the family have been tested through real data set.
We introduce a new lifetime distribution with six parameters. This distribution is called the add... more We introduce a new lifetime distribution with six parameters. This distribution is called the additive Weibull log logistic (AWLL) distribution based on the additive Weibull-generated family of distributions and the log logistic distribution as a baseline distribution. Important linear expansion forms for the cdf, pdf and reliability are obtained. Some statistical properties of the AWLL distribution including moments, incomplete moments, mean deviation, mode, median, skewness, and kurtosis are studied. Explicit expressions for the quantile function, moment-generating function and order statistics are obtained. The estimation of model parameters is discussed, using maximum likelihood method and the simulation study is conducted. The importance of the AWLL distribution is demonstrated through real data set compared with several lifetime distributions.
In this paper, we present a new family, depending on additive Weibull random variable as a genera... more In this paper, we present a new family, depending on additive Weibull random variable as a generator, called the generalized additive Weibull generated-family (GAW-G) of distributions with two extra parameters. The proposed family involves several of the most famous classical distributions as well as the new generalized Weibull-G family which already accomplished by Cordeiro et al. (2015). Four special models are displayed. The expressions for the incomplete and ordinary moments, quantile, order statistics, mean deviations, Lorenz and Benferroni curves are derived. Maximum likelihood method of estimation is employed to obtain the parameter estimates of the family. The simulation study of the new models is conducted. The efficiency and importance of the new generated family is examined through real data sets.
International Journal of Statistics and Probability, 2020
A goal of this research is providing new probability distribution called Sinh inverted exponentia... more A goal of this research is providing new probability distribution called Sinh inverted exponential distribution. The new distribution was extensively depending on the hyperbolic sine family of distributions with exponential distribution as a baseline distribution. Valuable statistical properties of the proposed distribution including mathematical and asymptotic expressions for its probability density function and Reliability. Moments, quantiles, moment generating function, failure rate function, mean residual lifetime, order statistics and entropies are derived. Actually, the applicability and validation of this model is proved in simulation study and an application to neck cancer disease data.
The Journal of Advanced Research in Applied Mathematics, 2019
We introduce a new lifetime distribution with six parameters. This distribution is called the add... more We introduce a new lifetime distribution with six parameters. This distribution is called the additive Weibull log logistic (AWLL) distribution based on the additive Weibull-generated family of distributions and the log logistic distribution as a baseline distribution. Important linear expansion forms for the cdf, pdf and reliability are obtained. Some statistical properties of the AWLL distribution including moments, incomplete moments, mean deviation, mode, median, skewness, and kurtosis are studied. Explicit expressions for the quantile function, moment-generating function and order statistics are obtained. The estimation of model parameters is discussed, using maximum likelihood method and the simulation study is conducted. The importance of the AWLL distribution is demonstrated through real data set compared with several lifetime distributions.
A new family of inverse probability distributions named inverse Rayleigh family is introduced to ... more A new family of inverse probability distributions named inverse Rayleigh family is introduced to generate many continuous distributions. The shapes of probability density and hazard rate functions are investigated. Some Statistical measures of the new generator including moments, quantile and generating functions, entropy measures and order statistics are derived. The Estimation of the model parameters is performed by the maximum likelihood estimation method. Furthermore, a simulation study is used to estimate the parameters of one of the members of the new family. The data application shows that the new family models can be useful to provide better fits than other lifetime models
Far East Journal of Mathematical Sciences (FJMS), 2019
This paper introduces a new generator for continuous distributions in three extra parameters. It ... more This paper introduces a new generator for continuous distributions in three extra parameters. It is called the generalized inverse Weibull generated (GIW-G) family of distributions. The paper also introduces selected special models of family and explicit expressions of the GIWG family. Important mathematical properties of the family are obtained, for example, quantile and generating functions, ordinary and incomplete moments, mean deviations and the expressions of order statistics. The parameter estimates of the family are calculated using the maximum likelihood method and the simulation study of a new model belonging to the GIW-G family is conducted. The efficiency and importance of the family have been tested through real data set.
International Journal of Statistics and Probability, 2020
A goal of this research is providing new probability distribution called Sinh inverted exponentia... more A goal of this research is providing new probability distribution called Sinh inverted exponential distribution. The new distribution was extensively depending on the hyperbolic sine family of distributions with exponential distribution as a baseline distribution. Valuable statistical properties of the proposed distribution including mathematical and asymptotic expressions for its probability density function and Reliability. Moments, quantiles, moment generating function, failure rate function, mean residual lifetime, order statistics and entropies are derived. Actually, the applicability and validation of this model is proved in simulation study and an application to neck cancer disease data.
In this article, a new four-parameter lifetime model named the Weibull quasi Lindley distribution... more In this article, a new four-parameter lifetime model named the Weibull quasi Lindley distribution based on the Weibull G-family is introduced. It is more flexible than several recently introduced lifetime distributions. Various structural properties of the new distribution are derived including moments, moment generating function, quantile function, reliability, hazard rate function and mean residual life. Expressions for the R´enyi, q-entropies and density function of order statistics are also obtained. The model parameters are estimated by the method of maximum likelihoodand the observed information matrix is determined. Two real data sets are presented to illustrate the advantage of the new distribution. In fact, the new model provides a better fit to this data than some of the most important distributions.
International Journal of Statistics and Probability, 2017
In this paper, we present a new family, depending on additive Weibull random variable as a genera... more In this paper, we present a new family, depending on additive Weibull random variable as a generator, called the generalized additive Weibull generated-family (GAW-G) of distributions with two extra parameters. The proposed family involves several of the most famous classical distributions as well as the new generalized Weibull-G family which already accomplished by Cordeiro et al. (2015). Four special models are displayed. The expressions for the incomplete and ordinary moments, quantile, order statistics, mean deviations, Lorenz and Benferroni curves are derived. Maximum likelihood method of estimation is employed to obtain the parameter estimates of the family. The simulation study of the new models is conducted. The efficiency and importance of the new generated family is examined through real data sets.
In this paper a new continuous distribution with extra two parameters called the Weibull exponent... more In this paper a new continuous distribution with extra two parameters called the Weibull exponentiated inverse Raleigh distribution is introduced. The new distribution based on the Weibull generated family of distributions and exponentiated inverse Raleigh distribution as a baseline distribution. Important linear expansion forms for the cdf, pdf and reliability are obtained. We investigate the shapes of the density and hazard rate function. Some statistical properties of the new distribution including moments, mean residual life, quantile and generating functions, median, skewness and kurtosis and order statistics are discussed. The estimation of the model parameters is performed by the maximum likelihood method. The importance of the new distribution is examined through real data application and the results show that the new distribution can be useful to provide better fits than other lifetime models.
The additive Weibull distribution is an extended version of the most widely used Weibull distribu... more The additive Weibull distribution is an extended version of the most widely used Weibull distribution which is a quite flexible model for analyzing lifetime data. In this paper, a new family of distributions called additive Weibull generated (AW-G) is defined and studied.The new family includes the Weibull-G family which was previously worked out by Bourguignon et al. [7]. Four sub-models are introduced and studied in some details. Explicit expressions for the ordinary moments, quantile, order statistics and reliability are obtained. The method of maximum likelihood is used to estimate the model parameters of the family. The additive Weibull-G family may serve as a viable alternative to other distributions for modeling data arising in various fields such as the physical and biological sciences, survival analysis and engineering. The importance of the additive Weibull-G family is concluded by means of two real data sets.
This research includes new probability distribution which is named beta inverted Lindley distribu... more This research includes new probability distribution which is named beta inverted Lindley distribution. Some useful functions of the proposed distribution are derived. Important mathematical expansions are investigated. Statistical measures including; quantiles, moments, incomplete moments, Renyi and s entropies are acquired. Extra statistical properties such as mean deviations, central of tendency measures, coefficient of variation, coefficients of skewness and kurtosis are defined. The Bonferroni and Lorenz curves are conducted and the stress- strength reliability is computed. The maximum likelihood method is used to estimate parameters of beta inverted Lindley distribution. The importance and significance of the introduced model are applied through failure times data set. The main aim behind generalization is to make more flexibility to the distribution so that more data can be analyzed using the new distribution. The model parameters are estimated using maximum likelihood estimat...
In this study, an extended exponentiated Pareto distribution is proposed. Some statistical proper... more In this study, an extended exponentiated Pareto distribution is proposed. Some statistical properties are derived. We consider maximum likelihood, least squares, weighted least squares and Bayesian estimators. A simulation study is implemented for investigating the accuracy of different estimators. An application of the proposed distribution to a real data is presented.
International Journal of Statistics and Probability, 2020
A goal of this research is providing new probability distribution called Sinh inverted exponentia... more A goal of this research is providing new probability distribution called Sinh inverted exponential distribution. The new distribution was extensively depending on the hyperbolic sine family of distributions with exponential distribution as a baseline distribution. Valuable statistical properties of the proposed distribution including mathematical and asymptotic expressions for its probability density function and Reliability. Moments, quantiles, moment generating function, failure rate function, mean residual lifetime, order statistics and entropies are derived. Actually, the applicability and validation of this model is proved in simulation study and an application to neck cancer disease data.
A new generalization of inverse Lindley distribution, called Kumaraswamy inverse Lindley is prese... more A new generalization of inverse Lindley distribution, called Kumaraswamy inverse Lindley is presented in this study. Some mathematical expressions are determined for the proposed distribution. Significant statistical measures are deduced including quantiles, generating functions, ordinary and incomplete moments, entropies, mean deviations, and order statistics. Some other properties like median, mean, variance, coefficient of variation, coefficients of skewness, and kurtosis are characterized. Moreover, stress-strength reliability is defined. A simulation study of the Kumaraswamy inverse distribution is introduced using maximum likelihood estimation and the performances of their estimates are compared through biases and mean square errors. The applicability and importance of the new distribution are illustrated through two real data sets. https://dx. Bu çalışmada, Kumaraswamy ters Lindley adı verilen ters Lindley dağılımının yeni bir genellemesi sunulmuştur. Önerilen dağılım için bazı matematiksel ifadeler belirlenmiştir. Nicelikler, üreten fonksiyonlar, sıradan ve eksik anlar, entropiler, ortalama sapmalar ve sıra istatistikleri dahil olmak üzere önemli istatistiksel ölçümler çıkarılmıştır. Medyan, ortalama, varyans, varyasyon katsayısı, çarpıklık katsayıları ve basıklık gibi diğer bazı özellikler karakterize edilmiştir. Dahası, gerilme mukavemeti güvenilirliği tanımlanmıştır. Kumaraswamy ters dağılımının bir simülasyon çalışması, maksimum olasılık tahmini kullanılarak tanıtılmış ve tahminlerinin performansları, önyargılar ve ortalama kare hataları ile karşılaştırılmıştır. Yeni dağıtımın uygulanabilirliği ve önemi iki gerçek veri seti ile gösterilmektedir. https://dx.
International Journal of Statistics and Probability, 2020
A goal of this research is providing new probability distribution called Sinh inverted exponentia... more A goal of this research is providing new probability distribution called Sinh inverted exponential distribution. The new distribution was extensively depending on the hyperbolic sine family of distributions with exponential distribution as a baseline distribution. Valuable statistical properties of the proposed distribution including mathematical and asymptotic expressions for its probability density function and Reliability. Moments, quantiles, moment generating function, failure rate function, mean residual lifetime, order statistics and entropies are derived. Actually, the applicability and validation of this model is proved in simulation study and an application to neck cancer disease data.
Far East Journal of Mathematical Sciences (FJMS) Volume 112, Issue 2, Pages 237 - 266 , 2019
This paper introduces a new generator for continuous distributions in three extra parameters. It ... more This paper introduces a new generator for continuous distributions in three extra parameters. It is called the generalized inverse Weibull generated (GIW-G) family of distributions. The paper also introduces selected special models of family and explicit expressions of the GIWG family. Important mathematical properties of the family are obtained, for example, quantile and generating functions, ordinary and incomplete moments, mean deviations and the expressions of order statistics. The parameter estimates of the family are calculated using the maximum likelihood method and the simulation study of a new model belonging to the GIW-G family is conducted. The efficiency and importance of the family have been tested through real data set.
We introduce a new lifetime distribution with six parameters. This distribution is called the add... more We introduce a new lifetime distribution with six parameters. This distribution is called the additive Weibull log logistic (AWLL) distribution based on the additive Weibull-generated family of distributions and the log logistic distribution as a baseline distribution. Important linear expansion forms for the cdf, pdf and reliability are obtained. Some statistical properties of the AWLL distribution including moments, incomplete moments, mean deviation, mode, median, skewness, and kurtosis are studied. Explicit expressions for the quantile function, moment-generating function and order statistics are obtained. The estimation of model parameters is discussed, using maximum likelihood method and the simulation study is conducted. The importance of the AWLL distribution is demonstrated through real data set compared with several lifetime distributions.
In this paper, we present a new family, depending on additive Weibull random variable as a genera... more In this paper, we present a new family, depending on additive Weibull random variable as a generator, called the generalized additive Weibull generated-family (GAW-G) of distributions with two extra parameters. The proposed family involves several of the most famous classical distributions as well as the new generalized Weibull-G family which already accomplished by Cordeiro et al. (2015). Four special models are displayed. The expressions for the incomplete and ordinary moments, quantile, order statistics, mean deviations, Lorenz and Benferroni curves are derived. Maximum likelihood method of estimation is employed to obtain the parameter estimates of the family. The simulation study of the new models is conducted. The efficiency and importance of the new generated family is examined through real data sets.
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