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In this paper, we propose a new three-parameter modified Burr XII distribution based on the standard Burr XII distribution and the composition technique developed by [14]. Among others, we show that this technique has the ability to... more
In this paper, we propose a new three-parameter modified Burr XII distribution based on the standard Burr XII distribution and the composition technique developed by [14]. Among others, we show that this technique has the ability to significantly increase the flexibility of the former Burr XII distribution, with respect to the density and hazard rate shapes. Also, complementary theoretical aspects are studied as shapes, asymptotes, quantiles, useful expansion, moments, skewness, kurtosis, incomplete moments, moments generating function, stochastic ordering, reliability parameter and order statistics. Then, a Monte Carlo simulation study is carried out to assess the performance of the maximum likelihood estimates of the modified Burr XII model parameters. Finally, three applications to real-life data sets are presented, with models comparisons. The results are favorable for the new modified Burr XII model.
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Mixture distribution of life time distribution occurs in many setting and play very important role in many practical applications. So this article is considered with the mixture of modified inverse Weibull distribution(MMIWD). Statistical... more
Mixture distribution of life time distribution occurs in many setting and play very important role in many practical applications. So this article is considered with the mixture of modified inverse Weibull distribution(MMIWD). Statistical properties of the model with some graphs of the density and application of real life data are discussed.
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In this article, Burr III distribution is proposed with a significantly improved functional form. This new modification has enhanced the flexibility of the classical distribution with the ability to model all shapes of hazard rate... more
In this article, Burr III distribution is proposed with a significantly improved functional form. This new modification has enhanced the flexibility of the classical distribution with the ability to model all shapes of hazard rate function including increasing, decreasing, bathtub, upside-down bathtub, and nearly constant. Some of its elementary properties, such as rth moments, sth incomplete moments, moment generating function, skewness, kurtosis, mode, ith order statistics, and stochastic ordering, are presented in a clear and concise manner. The well-established technique of maximum likelihood is employed to estimate model parameters. Middle-censoring is considered as a modern general scheme of censoring. The efficacy of the proposed model is asserted through three applications consisting of complete and censored samples.
In this paper, a new transmuted general family of distributions is introduced and studied. In particular , we obtain explicit expressions for the moments, the incomplete moments, the moment generating function, entropies measures and... more
In this paper, a new transmuted general family of distributions is introduced and studied. In particular , we obtain explicit expressions for the moments, the incomplete moments, the moment generating function, entropies measures and order statistics. Further, we introduce a bivariate extension of the new family. Some sub-models of the family are introduced, involving Burr, Gompertz, Weibull and gamma distributions. We discuss the different methods of estimation of the model parameters and a simulation study is investigated for one of the special models to check the asymptotic behavior of the estimates under all estimation methods. Further, the potentiality of the family is illustrated by fitting two real data sets to the mentioned sub-models.
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In this paper, we introduce a new class of distributions called Burr X family of distributions with one extra positive parameter to generalize any continuous baseline distribution. This class can yield flexible hazard rate shapes such as... more
In this paper, we introduce a new class of distributions called Burr X family of distributions with one extra positive parameter to generalize any continuous baseline distribution. This class can yield flexible hazard rate shapes such as increasing, decreasing, bathtub and upside-down bathtub. Some mathematical properties of the new class including ordinary and incomplete moments, quantile, generating functions, mean deviations, order statistics and entropy measures are obtained. The model parameters are estimated by the maximum likelihood method. A real data is analyzed to check the potentiality of the new class.
In this paper, a new four parameter lifetime distribution called the Topp Leone Weibull-Lomax distribution is introduced. Some mathematical properties of the new distribution are studied including the quantile function, ordinary and... more
In this paper, a new four parameter lifetime distribution called the Topp Leone Weibull-Lomax distribution is introduced. Some mathematical properties of the new distribution are studied including the quantile function, ordinary and incomplete moments, probability weighted moment, conditional moments, order statistics, stocastic ordering and stress strength reliability parameter. The regression model and the residual analysis for the new model are also investigated. The model parameters are estimated by using the maximum likelihood criterion and the behavior of these estimates are examined by conducting a simulation study. We prove empirically the importance and flexibility of the new distribution in modeling four data sets.
In this article, a new "odds generalized gamma-G" family of distributions, called the GG-G family of distributions, is introduced. We propose a complete mathematical and statistical study of this family, with a special focus on... more
In this article, a new "odds generalized gamma-G" family of distributions, called the GG-G family of distributions, is introduced. We propose a complete mathematical and statistical study of this family, with a special focus on the Frechet distribution as baseline distribution. In particular, we provide infinite mixture representations of its probability density function and its cumulative distribution function, the expressions for the Renyi entropy, the reliability parameter and the probability density function of ith order statistic. Then, the statistical properties of the family are explored. Model parameters are estimated by the maximum likelihood method. A regression model is also investigated. A simulation study is performed to check the validity of the obtained estimators. Applications on real data sets are also included, with favorable comparisons to existing distributions in terms of goodness-of-fit.
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This article introduces a new three-parameter Marshall-Olkin Burr-R (MOB-R) family which extends the generalize Burr-G class. Some of its general properties are discussed. One of its special models called the MOB-Lomax distribution is... more
This article introduces a new three-parameter Marshall-Olkin Burr-R (MOB-R) family which extends the generalize Burr-G class. Some of its general properties are discussed. One of its special models called the MOB-Lomax distribution is studied in detail for illustrative purpose. A modified chi-square test statistic is provided for right censored data from the MOB-L distribution. The model parameters are estimated via the maximum likelihood and simulation results are obtained to assess the behavior of the maximum likelihood approach. Applications to real data sets are provided to show the usefulness of the proposed MOB-Lomax distribution. The modified chi-square test statistic shows that the MOB-Lomax model can be used as a good candidate for analyzing real censored data.
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In this article, we propose a general family of distributions called odd Burr III G-negative binomial. Several properties of the family are reported, including quantile function, mixture representation of its density, cumulative... more
In this article, we propose a general family of distributions called odd Burr III G-negative binomial. Several properties of the family are reported, including quantile function, mixture representation of its density, cumulative distribution functions, moments, incomplete moments, moment generating function, mean deviations, deviations, stochastic ordering, entropies, and parameter estimation via maximum likelihood (ML) method. A simulation study is carried out to check the asymptotic behavior of the ML estimates. The flexibility of the governing members of this family is shown by the use of data modeling such that the corresponding density functions may be symmetric, right-skewed, or left-skewed and their hazard rate functions can be increasing, decreasing, bathtub, upside-down bathtub, or constant.
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We exhibit a general family of distributions named “Kumaraswamy odd Burr G family of distributions” with four additional parameters to generalize any existing baseline distribution. Some statistical properties of the family are derived,... more
We exhibit a general family of distributions named “Kumaraswamy odd Burr G family of distributions” with four additional parameters to generalize any existing baseline distribution. Some statistical properties of the family are derived, including rth moments, mth incomplete moments, moment generating function and entropies. The parameters of the family are estimated by the maximum likelihood (ML) method for complete sam- ples as well as censored samples. Some sub-models of the family are considered and it is noted that their density functions can be symmetric, left-skewed, right-skewed, unimodal, bimodal and their hazard rate functions can be increasing, decreasing, bathtub, upside- down bathtub and J-shaped. Simulation is carried out for one of the sub-models to check the asymptotic behavior of the ML estimates. Applications to reliability (complete and censored) data are carried out to check the usefulness of some sub-models of the family.
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In this work, we introduce a new Burr XII power series class of distributions, which is obtained by compounding exponentiated Burr XII and power series distributions and has a strong physical motivation. The new distribution contains... more
In this work, we introduce a new Burr XII power series class of distributions, which is obtained by compounding exponentiated Burr XII and power series distributions and has a strong physical motivation. The new distribution contains several important lifetime models. We derive explicit expressions for the ordinary and incomplete moments and generating functions. We discuss the maximum likelihood estimation of the model parameters. The maximum likelihood estimation procedure is presented. We assess the performance of the maximum likelihood estimators in terms of biases, standard deviations, and mean square of errors by means of two simulation studies. The usefulness of the new model is illustrated by means of three real data sets. The new proposed models provide consistently better fits than other competitive models for these data sets.
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ABSTRACT This paper proposes a new generator function based on the inverted Kumaraswamy distribution and introduces ‘generalized inverted Kumaraswamy-G’ family of distributions. We provide a comprehensive account of some of its... more
ABSTRACT This paper proposes a new generator function based on the inverted Kumaraswamy distribution and introduces ‘generalized inverted Kumaraswamy-G’ family of distributions. We provide a comprehensive account of some of its mathematical properties that include the ordinary and incomplete moments, quantile and generating functions and order statistics. The infinite mixture representations for probability density and cumulative distribution and entropy functions of the new family are also established. The density function of the ith-order statistics is expressed as an infinite linear combination of baseline densities and model parameters are estimated by maximum likelihood method. Four special models of this family are also derived along with their respective hazard rate functions. The maximum likelihood estimation (MLE) method is used to obtain the model parameters. Monte Carlo simulation experiments are executed to assess the performance of the ML estimators under the corresponding generated models while some data applications are also illustrated. The results of the study show that the proposed distribution is more flexible as compared to the baseline model. This distribution especially can be used to model symmetric, left-skewed, right-skewed and reversed-J data sets.
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In this paper, we introduce a new extended generalized Burr III family of distributions in the so- called T-Burr III {Y} family by using the quantile functions of a few popular distributions. We derive the general mathematical properties... more
In this paper, we introduce a new extended generalized Burr III family of distributions in the so- called T-Burr III {Y} family by using the quantile functions of a few popular distributions. We derive the general mathematical properties of this extended family including explicit expressions for the quantile function, Shannon entropy, moments and mean deviations. Three new Burr III sub-families are then investigated, and four new extended Burr III models are discussed. The density of Burr III extended distributions can be symmetric, left-skewed, right-skewed or reversed-J shaped, and the hazard rate shapes can be increasing, decreasing, bathtub and upside-down bathtub. The potentiality of the newly generated distributions is demonstrated through applications to censored and complete data sets.
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We introduce a new class of univariate continuous distribut ion called Odd Burr-G Poisson family of distributions (in sh ort OBGP). Four special sub models are considered odd Burr Weibu ll Poisson, odd Burr Lomax Poisson, odd Burr Gamma... more
We introduce a new class of univariate continuous distribut ion called Odd Burr-G Poisson family of distributions (in sh ort OBGP). Four special sub models are considered odd Burr Weibu ll Poisson, odd Burr Lomax Poisson, odd Burr Gamma Poisson an d odd Burr beta Poisson. We gave the mixture representation of the pdf and cdf of OBGP density, we also discuss the shapes of p df and hrf of POBG family. We gave a comprehensive treatment of math ematical properties, such as, the rth moment,sth incomplete moment, moment generating function and mean deviations. We also dis cussed the Renyi and Shannon entropies and stochastic order ing. The model parameters are estimated by using maximum likelihood method and the expression for ith order statistics are given. A special model Odd Burr Lomax Poisson is discussed in detail. Simulat ion is carried out by using monte carlo method, to check the pe rformance of the maximum likelihood estimates. Two real life data appl ications are carried out to check the efficiency of the propos ed family.
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We propose a new family of distributions called the generalized Burr-G (GBG) family of distributions motivated mainly for lifetime phenomenon. Some mathematical properties of the n ew family are obtained such as quantile function, linear... more
We propose a new family of distributions called the generalized Burr-G (GBG) family of distributions motivated mainly for lifetime phenomenon. Some mathematical properties of the n ew family are obtained such as quantile function, linear rep esentation of the family density, moments and incomplete moments, mome nt g nerating function, mean deviations, stochastic order ing, stressstrength reliability parameter and order statistics. The m odel parameters are estimated by the method of maximum likel ihood for complete and censored samples. Four special models are disc ussed and the properties of one special model, the generalized Burruniform (GBU), are obtained. A simulation study is carried out to check the performance of maximum likelihood estimators. The usefulness of GBU model is proved empirically by means of thr ee real lifetime applications to complete and censored samp les.
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In this article, we propose a new family of distributions cal led odd Burr-III family of distributions generated from the logit of Burr-III random variable. We display density and hazard r ate plots of four special distributions of this... more
In this article, we propose a new family of distributions cal led odd Burr-III family of distributions generated from the logit of Burr-III random variable. We display density and hazard r ate plots of four special distributions of this new family an d found it very flexible with respect to density and hazard rate shapes. The f amily density can also be expressed as a linear combination o f exponentiated-G densities of the baseline distribution. W e obtain some mathematical properties of this new family suc h as quantile function, moments and incomplete moments, moment generati g function, mean deviations, Shannon entropy, stress-str ength reliability and the density of order statistics. The model p arameters are obtained by employing the method of maximum li kelihood. The mathematical properties of a special model of this famil y, the odd Burr-III-Lomax (OBIIILx) distribution are obtained and its usefulness is illustrated for uncensored and censored data sets.
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In this paper MML estimator and ML estimator of Weibull distribution by using doubly type II censored sample have been derived and compared in term of asymptotic variances and mean square error. The purpose of conducting the empirical... more
In this paper MML estimator and ML estimator of Weibull distribution by using doubly type II censored sample have been derived and compared in term of asymptotic variances and mean square error. The purpose of conducting the empirical study is to see the closeness of MML estimators to ML estimator, and relative efficiency of censored sample to complete sample.
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Abstract In this study, a new family of distributions called the type II Topp-Leone is introduced and three new special models are presented. Some mathematical properties of the type II Topp-Leone family are studied. Explicit expressions... more
Abstract In this study, a new family of distributions called the type II Topp-Leone is introduced and three new special models are presented. Some mathematical properties of the type II Topp-Leone family are studied. Explicit expressions for the moments, probability weighted, quantile function, mean deviation, order statistics, Rènyi and Shannon entropies are investigated. Parameter estimates of the family are obtained based on the maximum likelihood procedure for both uncensored and censored data. A simulation study is conducted to show the performance of the new family. Then, two real data sets based on censored and uncensored data sets are employed to show the usefulness of the new family.
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In this paper, we propose a new three-parameter modified Burr XII distribution based on the standard Burr XII distribution and the composition technique developed by [14]. Among others, we show that this technique has the ability to... more
In this paper, we propose a new three-parameter modified Burr XII distribution based on the standard Burr XII distribution and the composition technique developed by [14]. Among others, we show that this technique has the ability to significantly increase the flexibility of the former Burr XII distribution, with respect to the density and hazard rate shapes. Also, complementary theoretical aspects are studied as shapes, asymptotes, quantiles, useful expansion, moments, skewness, kurtosis, incomplete moments, moments generating function, stochastic ordering, reliability parameter and order statistics. Then, a Monte Carlo simulation study is carried out to assess the performance of the maximum likelihood estimates of the modified Burr XII model parameters. Finally, three applications to real-life data sets are presented, with models comparisons. The results are favorable for the new modified Burr XII model.