Search

In this article, we introduce a robust generalization of the generalized Topp-Leone-G (GEN-TL-G) family of distributions via the heavy-tailed technique, namely, heavy-tailed generalized Topp-Leone-G (HT-GEN-TL-G) family of distributions. Statistical properties of the HT-GEN-TL-G family of distributions including reliability functions, quantile function, density expansion, moments, moment generating function, incomplete moments, Rényi entropy, distribution of order statistics are derived. Different estimation methods including Maximum Likelihood, Anderson-Darling, Ordinary Least Squares, Weighted Least Squares, Cramér-von Mises and Maximum Product of Spacing are utilized to estimate the unknown parameters of the new distribution, and a simulation study is used to compare the results of the estimation methods. Risk measures for this distribution were also developed and finally the effectiveness of this new family of distributions was demonstrated using applications to two real data sets. Graphical and application results in this manuscript were obtained using R programming language. [ABSTRACT FROM AUTHOR]

Order statistics occupy an important place in statistical theory. They have an important place in many fields of applied statistics such as goodness of fit tests and parameter estimation. In addition, it is necessary to find the expected values of these order statistics in these application areas. However for some probability distributions, these expected values are very difficult to find such as the standard normal distribution. So the problem of finding the expected values of the order statistics in statistical theory is of importance. In this study, two novel approximation methods are proposed for the expected values of the order statistics of the standard normal distribution. Also, the true values with previously given approximations, simulation results and our proposed approximations are compared by using mean square error (MSE), mean absolute error (MAE) and maximum error (ME) criteria. Furthermore, to evaluate the performances of all approximation methods, we compute the differences between exact values and approximation values. Then, the plot of these differences against the exact values is given. Based on both the plots and the comparison results, novel approximations fit the true values better than the other approximations presented in this paper. [ABSTRACT FROM AUTHOR]

This paper introduces a new cubic transmutation of the inverse Weibull distribution, known as a cubic transmuted inverse Weibull distribution. The model is thought to be useful for the analysis of complex life data, modeling failure times, accessing product reliability, and many other fields like economics, hydrology, biology, and engineering. Some statistical features of the proposed distribution are explored. These include moments, generating functions, quantile functions, reliability functions, and hazard rate functions. The distribution of order statistics for the proposed cubic transmuted inverse Weibull distribution is also studied. The maximum likelihood estimation approach is used to estimate the model parameters. The effectiveness of the estimation is investigated through extensive simulation study. The suitability of the proposed distribution has been studied by using five real-life datasets. It is found that the proposed distribution is the most suitable fit for the used data sets. [ABSTRACT FROM AUTHOR]

In this paper, the unit Garima distribution is introduced. It is used for analysing proportional data. Some statistical properties of the proposed distribution are investigated, including survival and hazard functions, order statistics, quantile function, and stress-strength reliability measures. A new family of continuous distributions, called the unit Garima-generated family of distributions, is also provided. It used the unit Garima distribution as the main generator. Some sub-models of the unit Garima-generated family of distributions are provided, such as the unit Garima-beta, unit Garima-Weibull, and unit Garima-normal distributions. The method of maximum likelihood is used to estimate the model parameters. A Monte Carlo simulation is used to illustrate the performance of the percentile confidence interval construction for each parameter of the proposed distributions. Finally, the developed distributions are applied to eight real data sets. [ABSTRACT FROM AUTHOR]

This article introduces a new three-parameter model with an increasing and bathtub failure rate functions as an extension of the Mustapha type-II distribution (Mu-II). The model can be very useful in statistical studies, reliability, computer sciences and engineering. Various mathematical and statistical properties of the distribution are discussed, such as moments, mean deviations, Bonferroni and Lorenz curves, entropy, order statistic, and extreme value distributions. Moreover, we consider the bivariate extension of the new model. Statistical inferences by the maximum likelihood method are discussed and assess by simulation studies. Applications of the proposed model to two rightskewed data are presented for illustration. The new model provides a better fit than some other existing distribution as measured by some model selection criteria and goodness of fits statistics. [ABSTRACT FROM AUTHOR]

The Kumaraswamy distribution is an important probability distribution used to model several hydrological problems as well as various natural phenomena whose process values are bounded on both sides. In this paper, we have introduced a new family of distributions by using the inverse Kumaraswamy distribution. The statistical properties of the proposed family of distributions have been explored. The maximum likelihood estimation of the new proposed family of distributions have been discussed by using the random sample and the dual generalized order statistics. A particular sub-model of this family; namely, the inverse Kumaraswamy-Weibull distribution, is considered and some of its statistical properties are obtained. Estimation efficiency is numerically evaluated via a simulation study and two real-data applications of the proposed distribution are provided as well. [ABSTRACT FROM AUTHOR]

The present study deals with a new version of power quasi Lindley distribution known as weighted power quasi Lindley distribution. Its different mathematical and statistical properties like moments, order statistics, reliability analysis, Renyi entropy, bonferroni and Lorenz curves have been presented. The parameters of proposed new distribution are estimated by employing the method of maximum likelihood estimation. Finally, a new distribution has been illustrated with three real lifetime data sets from medical sciences to examine its significance and supremacy. [ABSTRACT FROM AUTHOR]

Weighted distributions play an important role when observations from a sample are recorded with unequal probabilities. They are useful for the efficient modeling of statistical data when the original distributions are not appropriate. In this paper, a new weighted distribution is proposed. Various statistical properties of the proposed distribution such as survival function, hazard rate function, mean residual life function, moments, moment generating function, Bonferroni curve, Lorenz curve, and order statistic are presented. The Bayesian estimator of the distribution parameter is derived. The behavior of the Bayesian estimator is assessed by a simulation study. Furthermore, a regression model is developed based on the proposed distribution. Some real data applications are analyzed to show the potentiality of the proposed models. [ABSTRACT FROM AUTHOR]

This paper introduced a new life time data analysis distribution name three parameters quasi gamma distribution discussed about its some properties including moment generating function, rth moment about origin and mean, mean deviations, reliability measurements, Bonferroni and Lorenz curve, Order statistics, Renyi entropy, also discussed about maximum likelihood method and real-life data applications. [ABSTRACT FROM AUTHOR]

This paper introduces a novel alpha power exponentiated Weibull-Pareto distribution based on the alpha power transformation. We derive several properties of the new distribution, including moments, quantile function, mean residual life, mean waiting time, and order statistics. Estimating model parameters is performed using the method of maximum likelihood. Then, for the purpose of evaluating the effectiveness of the estimates, we conduct some simulation studies. Finally, we demonstrate the superiority of this new model by analyzing three real-life data sets. [ABSTRACT FROM AUTHOR]

In this paper, we proposed a new generalized family of distribution namely new alpha power Exponential (NAPE) distribution based on the new alpha power transformation (NAPT) method by Elbatal et al. (2019). Various statistical properties of the proposed distribution are obtained including moment, incomplete moment, conditional moment, probability weighted moments (PWMs), quantile function, residual and reversed residual lifetime function, stress-strength parameter, entropy and order statistics. The percentage point of NAPE distribution for some specific values of the parameters is also obtained. The method of maximum likelihood estimation (MLE) has been used for estimating the parameters of NAPE distribution. A simulation study has been performed to evaluate and execute the behavior of the estimated parameters for mean square errors (MSEs) and bias. Finally, the efficiency and flexibility of the new proposed model are illustrated by analyzing three real-life data sets. [ABSTRACT FROM AUTHOR]

In recent years, researchers focused on introducing discrete type distributions which satisfy the necessary demand to model the complex performance of the real data sets. In this paper, a discrete inverted Kumaraswamy distribution, which is a discrete version of the continuous inverted Kumaraswamy distribution, is derived using the general approach of discretization of a continuous distribution. The new discrete inverted Kumaraswamy distribution can be applied efficiently in discrete lifetime and count data. Some important distributional and reliability properties of discrete inverted Kumaraswamy distribution such as hazard rate, moments, quantiles, order statistics and some transformations are obtained. Maximum likelihood and Bayesian approaches are applied under Type-II censored samples for estimating the parameters, survival, hazard rate and alternative hazard rate functions. Confidence and credible intervals for the parameters are obtained. A simulation study is carried out to illustrate the theoretical results of the maximum likelihood and Bayesian estimation. Finally, the performance of the new distribution is compared with some distributions using three real data sets to illustrate the suitability and flexibility of the proposed model. [ABSTRACT FROM AUTHOR]

In this paper, a new mixture distribution for count data, namely the negative binomial-new generalized Lindley (NB-NGL) distribution is proposed. The NB-NGL distribution has four parameters, and is a flexible alternative for analyzing count data, especially when there is over-dispersion in the data. The proposed distribution has submodels such as the negative binomial-Lindley (NB-L), negative binomial-gamma (NB-G), and negative binomialexponential (NB-E) distributions as the special cases. Some properties of the proposed distribution are derived, i.e., the moments and order statistics density function. The unknown parameters of the NB-NGL distribution are estimated by using the maximum likelihood estimation. The results of the simulation study show that the maximum likelihood estimators give the parameter estimates close to the parameter when the sample is large. Application of NB-NGL distribution is carry out on three samples of medical data, industry data, and insurance data. Based on the results, it is shown that the proposed distribution provides a better fit compared to the Poisson, negative binomial, and its sub-model for count data. [ABSTRACT FROM AUTHOR]

In this paper, we use the concept of dual generalized order statistics dgos which was given by Pawlas and Syznal (2001). By using this, we obtain the various theorems and some relations through ratio and inverse moment by using exponentiated-Weibull distribution. Cases for order statistics and lower record values are also considered. Further, we characterize the exponentiated-Weibull distribution through three different methods by using the results obtained in this paper. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new flexible lifetime distribution. The proposed distribution will be referred to as beta power Muth distribution. It can be used to model increasing, decreasing, bathtub shaped or upside-down bathtub hazard rates. Some properties of the new model are obtained including moments, quantile function and moments of the order statistics. The unknown model parameters are estimated by the maximum likelihood method of estimation. A Monte Carlo simulation study is carried out to assess the performance of the maximum likelihood estimates. Two reliability data sets are applied to illustrate the usefulness and flexibility of the proposed model. In addition, we introduce a new location-scale regression model based on the logarithm of the proposed distribution and provide a real data application. [ABSTRACT FROM AUTHOR]

In this paper, we have proposed a new family of distributions namely the Pareto-X family of distributions. A sub model of the proposed family called Pareto-Weibull (PW) distribution is discussed. Some important properties of the proposed PW distribution are studied. Parameter estimation of the distribution by using the maximum likelihood method is discussed. The proposed distribution has been fitted on two real data sets about environmental and biological variable. The practical applications shows that the proposed model provides better fit as compared with the other models used in the study. [ABSTRACT FROM AUTHOR]

We propose the McDonald Lindley-Poisson distribution and derive some of its mathematical properties including explicit expressions for moments, generating and quantile functions, mean deviations, order statistics and their moments. Its model parameters are estimated by maximum likelihood. A simulation study investigates the performance of the estimates. The new distribution represents a more flexible model for lifetime data analysis than other existing models as proved empirically by means of two real data sets. [ABSTRACT FROM AUTHOR]

In this paper, we developed a new distribution, namely the two parameters Rani distribution (TPRD). Some statistical properties of the proposed distribution are derived including the moments, moment-generating function, reliability function, hazard function, reversed hazard function, odds function, the density function of order statistics, stochastically ordering, and the entropies. The maximum likelihood method is used for model parameters estimation. Following the same approach suggested by Bagdonavicius and Nikulin (2011), modified chi squared goodness-of-fit tests are constructed for right censored data and some tests for right data is considered. An application study is presented to illustrate the ability of the suggested model in fitting aluminum reduction cells sets and the strength data of glass of the aircraft window. [ABSTRACT FROM AUTHOR]

In this paper, a new probability discrete distribution for analyzing over-dispersed count data encountered in biological sciences was proposed. The new discrete distribution, with one parameter, has a log-concave probability mass function and an increasing hazard rate function, for all choices of its parameter. Several properties of the proposed distribution including the mode, moments and index of dispersion, mean residual life, mean past life, order statistics and Lmoment statistics have been established. Two actuarial or risk measures were derived. The numerical computations for these measures are conducted for several parametric values of the model parameter. The parameter of the introduced distribution is estimated using eight frequentist estimation methods. Detailed Monte Carlo simulations are conducted to explore the performance of the studied estimators. The performance of the proposed distribution has been examined by three over-dispersed real data sets from biological sciences. [ABSTRACT FROM AUTHOR]

In this paper, relations between moments of dual generalized order statistics from a exponentiated generalized class of distributions, given by Cardeiro . et al (2013) are studied. Some particular cases of dual generalized order statistics and examples based on it are discussed. The characterization of given distribution based on moment properties is also presented. [ABSTRACT FROM AUTHOR]

A new four-parameter lifetime model is introduced and studied. The new model derives its flexibility and wide applicability from the well-known exponentiated Weibull model. Many bivariate and the multivariate type versions are derived using the Morgenstern family and Clayton copula. The new density can exhibit many important shapes with different skewness and kurtosis which can be unimodal and bimodal. The new hazard rate can be decreasing, J-shape, U-shape, constant, increasing, upside down and increasing-constant hazard rates. Various of its structural mathematical properties are derived. Graphical simulations are used in assessing the performance of the estimation method. We proved empirically the importance and flexibility of the new model in modeling various types of data such as failure times, remission times, survival times and strengths data. [ABSTRACT FROM AUTHOR]

In this article, an extension of the transmuted-G family is proposed, in the so-called Poison transmuted-G family of distributions. Some of its statistical properties including quantile function, moment generating function, order statistics, probability weighted moment, stress-strength reliability, residual lifetime, reversed residual lifetime, Rényi entropy and mean deviation are derived. A few important special models of the proposed family are listed. Stochastic characterizations of the proposed family based on truncated moments, hazard function and reverse hazard function, are also studied. The family parameters are estimated via the maximum likelihood approach. A simulation study is carried out to examine the bias and mean square error of the maximum likelihood estimators. The advantage of the proposed family in data fitting is illustrated by means of two applications to failure time data sets. [ABSTRACT FROM AUTHOR]

In this paper, we present simple explicit expressions for single and product moments of generalized order statistics from generalized Pareto distribution. These relations are deduced for the moments of order statistics and record values and tabulated the mean and variance of this distribution. Further, conditional expectation, recurrence relations for single as well as for product moments of generalized order statistics and truncated moment are used to characterize this distribution. [ABSTRACT FROM AUTHOR]

For a non-negative continuous random variable 𝑋, Chaudhry and Zubair (2002) introduced a probability distribution with a completely monotonic probability density function based on the generalized gamma function, and called it the Macdonald probability function. In this paper, we establish various basic distributional properties of Chaudhry and Zubair's Macdonald probability distribution. Since the percentage points of a given distribution are important for any statistical applications, we have also computed the percentage points for different values of the parameter involved. Based on these properties, we establish some new characterization results of Chaudhry and Zubair's Macdonald probability distribution by the left and right truncated moments, order statistics and record values. Characterizations of certain other continuous probability distributions with completely monotonic probability density functions such as Mckay, Pareto and exponential distributions are also discussed using the proposed characterization techniques. [ABSTRACT FROM AUTHOR]

A new flexible extension of the Fréchet model is proposed and studied. Some of its fundamental statistical properties are derived. The importance of the new model is shown via two applications to real data sets. We assess the performance of the maximum likelihood estimations of the new distribution with respect to sample size n. The assessment was based on a simulation study. The new model is much better than other important competitive models. [ABSTRACT FROM AUTHOR]

In this Paper, we have introduced a new version of new quasi Lindley distribution known as the length-biased weighted new quasi Lindley distribution (LBWNQLD). The length biased distribution is a special case of weighted distribution. The different mathematical and statistical properties of the newly proposed distribution are derived and discussed in detail. The model parameters of the newly executed distribution are estimated by using the method of maximum likelihood estimation and also the Fisher's information matrix have been discussed. Finally, an application of the proposed distribution is demonstrated with two real life data sets for illustrating its supremacy and applicability. [ABSTRACT FROM AUTHOR]

The relations for moments of generalized order statistics (gos) for transmuted exponential distribution are obtained. These include relations for single, inverse, product and ratio moments. These relations are useful in for recursive computation of moments of gos for transmuted exponential distribution. Some characterizations of the distribution, based on single and product moments of gos, are also obtained. [ABSTRACT FROM AUTHOR]

In this paper, the shape parameters, reliability and hazard rate functions of the inverted Kumaraswamy distribution are estimated using maximum likelihood and Bayesian methods based on dual generalized order statistics. The Bayes estimators are derived under the squared error loss function as a symmetric loss function and the linear-exponential loss function as an asymmetric loss function based on dual generalized order statistics. Confidence and credible intervals for the parameters, reliability and hazard rate functions are obtained. All results are specialized to lower record values, also a numerical study is presented to illustrate the theoretical procedures. [ABSTRACT FROM AUTHOR]

A new three-parameter life parametric model called the Marshall-Olkin generalized Weibull is defined and studied. Relevant properties are mathematically derived and analyzed. The new density exhibits various important symmetric and asymmetric shapes with different useful kurtosis. The new failure rate can be "constant", "upside down-constant (reversed U-HRF-constant)", "increasing then constant", "monotonically increasing", "J-HRF" and "monotonically decreasing". The method of maximum likelihood is employed to estimate the unknown parameters. A graphical simulation is performed to assess the performance of the maximum likelihood estimation. We checked and proved empirically the importance, applicability and flexibility of the new Weibull model in modeling various symmetric and asymmetric types of data. The new distribution has a high ability to model different symmetric and asymmetric types of data. [ABSTRACT FROM AUTHOR]

The truncated distributions have been widely studied, mainly in life-testing and reliability analysis. In this paper, we introduce a new right truncated generator related to power Lomax distribution, referred to right truncated power Lomax--G family. The proposed family is a generalization of recently [0, 1] truncated Lomax-G family. Statistical properties like; moments, moment generating function, probability weighted moments, quantile function, mean deviation, order statistics and Rényi entropy are derived. Five new sub-models from the truncated family are presented. Maximum likelihood estimation is investigated and simulation issues are discussed for truncated power Lomax Weibull model as particular case from the family. The flexibility of the truncated power Lomax Weibull is assessed by applying it to a real data set. The application indicates that the truncated power Lomax Weibull distribution model can give better fits than other well-known lifetime distributions. [ABSTRACT FROM AUTHOR]

This paper is devoted to study a new four-parameter additive model. The newly suggested model is referred to as the flexible Weibull extension-Burr XII distribution. It is derived by considering a serial system with one component following a flexible Weibull extension distribution and another following a Burr XII distribution. The usefulness of the model stems from the flexibility of its failure rate which accommodates bathtub and modified bathtub among other risk patterns. These two patterns have been widely accepted in several fields, especially reliability and engineering fields. In addition, the importance of the new distribution is that it includes new submodels which are not known in the literature. Some statistical properties of the proposed distribution such as quantile function, the mode, the rth moment, the moment generating function and the order statistics are discussed. Moreover, the method of maximum likelihood is used to estimate the parameters of the model. Also, to evaluate the performance of the estimators, a simulation study is carried out. Finally, the performance of the proposed distribution is compared through a real data set to some well-known distributions including the new modified Weibull, the additive Burr and the additive Weibull distributions. It is shown that the proposed model provides the best fit for the used real data set. [ABSTRACT FROM AUTHOR]

A new univariate extension of the Fréchet distribution is proposed and studied. Some of its fundamental statistical properties such as stochastic properties, ordinary and incomplete moments, moments generating functions, residual life and reversed residual life functions, order statistics, quantile spread ordering, Rényi, Shannon and q-entropies are derived. A simple type Copula based construction using Morgenstern family and via Clayton Copula is employed to derive many bivariate and multivariate extensions of the new model. We assessed the performance of the maximum likelihood estimators using a simulation study. The importance of the new model is shown by means of two applications to real data sets. [ABSTRACT FROM AUTHOR]

This work proposes an inverse odd Weibull (IOW) family of distributions for a lifetime distributions. Some mathematical properties of this family of distribution were derived. Survival, hazard, quantiles, reversed hazard, cumulative, odd functions, kurtosis, skewness, order statistics and entropies of this new family of distribution were examined. The parameters of the family of distributions were obtained by maximum likelihood. The behavior of the estimators were studied through simulation. The flexibility and importance of the distribution by means of real data set applications were emphasized. [ABSTRACT FROM AUTHOR]

In this article, we propose a new four-parameter Fréchet distribution called the odd Lomax Fréchet distribution. The new model can be expressed as a linear mixture of Fréchet densities. We provide some of its mathematical properties. The estimation of the model parameters is performed by the maximum likelihood method. We illustrate the good performance of the maximum likelihood estimates via a detailed numerical simulation study. The importance and usefulness of the proposed distribution for modeling data are illustrated using two real data applications. [ABSTRACT FROM AUTHOR]

We study a new family of distributions defined by the minimum of the Poisson random number of independent identically distributed random variables having a Topp Leone-G distribution (see Rezaei et al., (2016)). Some mathematical properties of the new family including ordinary and incomplete moments, quantile and generating functions, mean deviations, order statistics, reliability and entropies are derived. Maximum likelihood estimation of the model parameters is investigated. Some special models of the new family are discussed. An application is carried out on real data set applications sets to show the potentiality of the proposed family. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new version of the power Lindley distribution known as weighted power Lindley distribution. The different structural properties of the new model are studied such as moments, generating functions, likelihood ratio test, entropy measures and order statistics. The maximum likelihood estimators of the parameters and the Fisher's information matrix are discussed. It also provides more flexibility to analyse complex real data sets. Applications of the model to real data sets are provided using the new distribution, which shows that the weighted power Lindley distribution can be used quite effectively in analysing real life time data. [ABSTRACT FROM AUTHOR]

We study a new family of distributions defined by the minimum of the Poisson random number of independent identically distributed random variables having a general Weibull-G distribution (see Bourguignon et al. (2014)). Some mathematical properties of the new family including ordinary and incomplete moments, quantile and generating functions, mean deviations, order statistics, reliability and entropies are derived. Maximum likelihood estimation of the model parameters is investigated. Three special models of the new family are discussed. We perform three applications to real data sets to show the potentiality of the proposed family. [ABSTRACT FROM AUTHOR]

A new family of distributions called the odd generalized N-H is introduced and studied. Four new special models are presented. Some mathematical properties of the odd generalized N-H family are studied. Explicit expressions for the moments, probability weighted, quantile function, mean deviation, order statistics and Rényi entropy are investigated. Characterizations based on the truncated moments, hazard function and conditional expectations are presented for the generated family. Parameter estimates of the family are obtained based on maximum likelihood procedure. Two real data sets are employed to show the usefulness of the new family. [ABSTRACT FROM AUTHOR]

In this paper a new inverse Kumaraswamy distribution has been proposed. The recurrence relation for moments of dual generalized order statistics has been presented for the new inverse Kumaraswamy distribution. These include the recurrence relations for single, inverse, product and ratio moments of dual generalized order statistics for the new inverse Kumaraswamy distribution. Special cases of the recurrence relations have also been obtained. [ABSTRACT FROM AUTHOR]

A new univariate extension of the Inverse Rayleigh distribution is proposed and studied. Some of its fundamental statistical properties such as some stochastic properties, ordinary and incomplete moments, moments generating functions, residual life and reversed residual life functions, order statistics, quantile spread ordering, Rényi, Shannon and q-entropies are derived. A simple type Copula based construction via Morgenstern family and via Clayton copula is employed to derive many bivariate and multivariate extensions of the new model. We assessed the performance of the maximum likelihood estimators using a simulation study. The importance of the new model is shown via two applications to real data sets. [ABSTRACT FROM AUTHOR]

Based on the Nadarajah Haghighi distribution and the Topp Leone-G family in view of the T-X family, we introduce a new generator of continuous distributions with three extra parameters called the Nadarajah Haghighi Topp Leone-G family. Three sub-models of the new class are discussed. Main mathematical properties of the new family are investigated such as; quantile function, raw and incomplete moments, Bonferroni and Lorenz curves, moment and probability generating functions, stress strength model, Shanon and Rényi entropies, order statistics and probability weighted moments. The model parameters of the new family is estimated by using the method of maximum likelihood and the observed information matrix is also obtained. We introduce two real applications to show the importance of the new family. [ABSTRACT FROM AUTHOR]

We propose an alternative two-phase stratified ranked set sampling. A comparison of the performances of the proposed estimators made by simulation studies using both real and simulated data sets. It is found that the proposed two-phase stratified regression estimator beats its competitors in literature. [ABSTRACT FROM AUTHOR]

Mahdavi and Kundu (2017) introduced a family for generating univariate distributions called the alpha power transformation. They studied as a special case the properties of the alpha power trans- formed exponential distribution. We provide some mathematical properties of this distribution and define a four-parameter lifetime model called the alpha power exponentiated Weibull distribution. It generalizes some well-known lifetime models such as the exponentiated exponential, exponentiated Rayleigh, exponentiated Weibull and Weibull distributions. The importance of the new distribution comes from its ability to model monotone and non-monotone failure rate functions, which are quite common in reliability studies. We derive some basic properties of the proposed distribution including quantile and generating functions, moments and order statistics. The maximum likelihood method is used to estimate the model parameters. Simulation results investigate the performance of the estimates. We illustrate the importance of the proposed distribution over the McDonald Weibull, beta Weibull, modified Weibull, transmuted Weibull and exponentiated Weibull distributions by means of two real data sets. [ABSTRACT FROM AUTHOR]

In this paper, we investigate a new model based on Burr X and Fréchet distributions for extreme values and derive some of its properties. Maximum likelihood estimation along with asymptotic confidence intervals is considered for estimating the parameters of the distribution. We demonstrate empirically the flexibility of the distribution in modeling various types of real data. Furthermore, we also provide Bayes estimators and highest posterior density (HPD) intervals of the parameters of the distribution using Markov Chain Monte Carlo (MCMC) methods. [ABSTRACT FROM AUTHOR]

This paper focuses on the Bayesian prediction of kth ordered future observations modelled by a two-component mixture of general class of distributions. Samples under consideration are subject to random censoring. A closed form of Bayesian predictive density is obtained under a two-sample scheme. Applications to Weibull and Burr XII components are presented and comparisons with previous results are made. A numerical example is presented for special cases of the exponential and Lomax components to obtain interval prediction of first and last order statistics. A simulation study has been conducted to assess the effect of sample size, hyper parameters, and level of censoring on prediction interval and point prediction of a future observation coming from the two-component exponential model. [ABSTRACT FROM AUTHOR]

This article introduces a new lifetime model called the generalized transmuted-Kumaraswamy distribution which extends the Kumaraswamy distribution from the family proposed by Nofal et al., (2017). We provided hazard and survival functions of the proposed distribution. The statistical properties of the proposed distribution are provided and the method of Maximum Likelihood Estimation (MLE) was proposed in estimating its parameters. [ABSTRACT FROM AUTHOR]

In this paper, a new class of continuous distributions with two extra positive parameters is introduced and is called the Type II General Exponential (TIIGE) distribution. Some special models are presented. Asymptotics, explicit expressions for the ordinary and incomplete moments, moment residual life, reversed residual life, quantile and generating functions and stress-strengh reliability function are derived. Characterizations of this family are obtained based on truncated moments, hazard function, conditional expectation of certain functions of the random variable are obtained. The performance of the maximum likelihood estimators in terms of biases, mean squared errors and confidence interval length is examined by means of a simulation study. Two real data sets are used to illustrate the application of the proposed class. [ABSTRACT FROM AUTHOR]

In this paper, we develop a new lifetime model and study some of its properties. The major justification for the practicality of theis model is based on the wider use of the Lomax model. We are also motivated to introduce the novel model since its density exhibits various important shapes such as the unimodal, right skewed and left skewed. The new model can be represented as a mixture of the exponentiated Lomax distribution. It can also be considered as a suitable model for fitting the symmetric, left skewed, right skewed and unimodal data. The maximum likelihood estimation method is used to estimate the model parameters. We show empirically the importance and flexibility of the novel model in modeling two types of aircraft windshield lifetime data sets. The proposed lifetime model is better fit than gamma Lomax, beta Lomax, exponentiated Lomax and Lomax models so the exponentiated Lomax, model is a good alternative to these models in modeling aircraft windshield data. [ABSTRACT FROM AUTHOR]

In this paper, a new four parameter lifetime model with increasing, decreasing, increasingdecreasing, decreasing-increasing-decreasing, modified bathtub, bathtub and inverted bathtub hazard rate function called Burr III-Pareto (BIII-Pareto) is developed on the basis of the T-X family technique. The BIII-Pareto density function is arc, J-shape, reverse J-shape, positively, negatively skewed and symmetrical. Some structural and mathematical properties including moments, moments of order statistics, inequality measures and reliability measures are theoretically established. The BIII-Pareto distribution is characterized via different techniques. Parameters of the BIII-Pareto distribution are estimated using maximum likelihood method. The simulation study for performance of the maximum likelihood estimates (MLEs) of parameters for the BIII-Pareto distribution is carried out. The potentiality of the BIII-Pareto distribution is demonstrated by its application to real data sets. Goodness of fit of this distribution through different methods is studied. The BIII-Pareto distribution is empirically better for lifetime applications. [ABSTRACT FROM AUTHOR]

In this article, we present a new generalization of weighted Weibull distribution using Topp Leone family of distributions. We have studied some statistical properties of the proposed distribution including quantile function, moment generating function, probability generating function, raw mo-ments, incomplete moments, probability, weighted moments, Rayeni and q - th entropy. We have obtained numerical values of the various measures to see the effect of model parameters. Distribu-tion of order statistics for the proposed model has also been obtained. The estimation of the model parameters has been done by using maximum likelihood method. The effectiveness of proposed model is analyzed by means of a real data sets. Finally, some concluding remarks are given. [ABSTRACT FROM AUTHOR]