Incomplete Moments Research Articles

A Generalized Transmuted Moment Exponential Distribution: Properties and Application

This paper introduces a new generalization of moment exponential (or length biased) distribution. The new model is referred to as generalized transmuted moment exponential distribution. This model contains some new existing distributions. Structural properties of the suggested distribution including closed forms for ordinary and incomplete moments, quantile and generating functions and Rényi entropy are derived. Maximum likelihood estimation is employed to obtain the parameter estimators of the new distribution. We illustrate the importance of the new model by means of three applications to real data sets.

Transmuted Burr Type X Distribution with Covariates Regression Modeling to Analyze Reliability Data

SYNOPTIC ABSTRACTThis article investigates the potential usefulness of the three-parameter transmuted Burr type X (TBX) distribution for modeling reliability data, and explore its structural properties using simulation. Explicit expressions are derived for moments, incomplete moments, entropies, and mean deviation. The method of maximum likelihood is used for estimating the model parameters. We conduct Monte Carlo simulations, which are used to examine the relative performance of the estimators using MLE in terms of bias and mean square errors. A location-scale regression model based on the log-TBX distribution is proposed for modeling lifetime data. Use of this family of distributions is illustrated for fatigue fracture data and multiple myeloma patient’s data.

A New Two-Parameter Lifetime Model

A new two parameter life time model, which accommodates increasing, decreasing, bathtub, and a broad variety of monotone failure rates, has been introduced in this article. Some of its mathematical properties including explicit expressions for the ordinary and incomplete moments, generating function, moment of residual and reversed residual lives have been derived. The maximum likelihood has been proposed for estimating the model parameters. The importance and flexibility of the new distribution has been illustrated by means of an applications to real data set supported by a Monte-Carlo simulation study.

The Topp Leone Generalized Inverted Kumaraswamy Distribution: Properties and Applications

We propose a new four parameters continuous model called the Topp Leone generalized inverted Kumaraswamy distribution which extends the generalized inverted Kumaraswamy distribution. Basic mathematical properties of the new distribution are invstigated such as; quantile function, raw and incomplete moments, generating functions, probability weighted moments, order statistics, Rényi entropy, stochastic ordering and stress strength model. The method of maximum likelihood is used to estimate the model parameters of the new distribution. A Monte Carlo simulation is conducted to examine the behavior of the parameter estimates. The applicability of the new model is demonstrated by means of two real applications.

A New Generalized Weighted Weibull Distribution

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 moments, incomplete moments, probability, weighted moments, Rayeni and q th entropy. The have obtained numerical values of the various measures to see the eect of model parameters. Distribution of 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 eectiveness of proposed model is analyzed by means of a real data sets. Finally, some concluding remarks are given.

On The Modified Burr XII-Power Distribution: Development, Properties, Characterizations and Applications

In this paper, a flexible lifetime distribution with increasing, decreasing and bathtub hazard rate called the Modified Burr XII-Power (MBXII-Power) is developed on the basis of the T-X family technique. The density function of the MBXII-Power is arc, exponential, left-skewed, right-skewed, J, reverse-J and symmetrical shaped. Descriptive measures such as moments, moments of order statistics, incomplete moments, inequality measures, residual life functions and reliability measures are theoretically established. The MBXII-Power distribution is characterized via different techniques. Parameters of the MBXII-Power distribution are estimated using maximum likelihood method. The simulation study is performed on the basis of graphical results to see the performance of maximum likelihood estimates (MLEs) of the MBXII-Power distribution. The potentiality of the MBXII-Power distribution is demonstrated by its application to real data sets: survival times of pigs, survival times of patients and quarterly earnings

The Exponentiated Generalized Topp Leone-G Family of Distributions: Properties and Applications

In this paper, we propose a new class of continuous distributions called the exponentiated generalized Topp Leone-G family that extends the Topp Leone-G family introduced by Al-Shomrani et al. (2016). We derive explicit expressions for certain mathematical properties of the new family such as; ordinary and incomplete moments, generating functions, reliability analysis, Lorenz and Bonferroni curves, Rényi entropy, stress strength model, moment of residual and reversed residual life, order statistics and extreme values. We discuss the maximum likelihood estimates and the observed information matrix for the model parameters. Two real data sets are used to illustrate the flexibility of the new family.

On modified Burr III-power distribution: Development, properties, characterizations, and applications

In this paper, a flexible distribution with increasing, bathtub and inverted bathtub hazard rate called Modified Burr III-Power (MBIII-Power) is developed on the basis of the generalized Pearson differential equation. The density function of MBIII-Power is arc, exponential and positively skewed shaped. Descriptive measures such as quantiles, moments, incomplete moments, inequality measures, residual life functions and reliability measures are theoretically established. The MBIII-Power distribution is characterized via different techniques. Parameters of MBIII-Power distribution are estimated using maximum likelihood method. The simulation study is performed to illustrate the performance of the maximum likelihood estimates (MLEs). Potential use of MBIII-Power distribution is demonstrated by its application to two data sets: serum-reversal time (in days) of children born from HIV-infected mothers and failure times of device data.

A New Zero-Truncated Version of the Poisson Burr XII Distribution: Characterizations and Properties

In this work, a new four-parameter zero-truncated Poisson Topp Leone Burr XII distribution is defined and studied. Various structural mathematical properties of the proposed model including ordinary and incomplete moments, residual and reversed residual life functions, generating functions, order statistics are investigated. Some useful characterizations are also presented.

EXPONENTIATED HALF-LOGISTIC LOMAX DISTRIBUTION WITH PROPERTIES AND APPLICATION

A new three-parameter continuous model called the exponentiated half-logistic Lomax distribution is introduced in this paper. Basic mathematical properties for the proposed model were investigated which include raw and incomplete moments, skewness, kurtosis, generating functions, Rényi entropy, Lorenz, Bonferroni and Zenga curves, probability weighted moment, stress strength model, order statistics, and record statistics. The model parameters were estimated by using the maximum likelihood criterion and the behaviours of these estimates were examined by conducting a simulation study. The applicability of the new model is illustrated by applying it on a real data set.

Some Remarks on Odd Burr III Weibull Distribution

In this study, a univariate model named as Odd Burr III Weibull distribution is developed. This study explains the behavior of the newly developed model and also presents its failure and survival rate functions. Moreover, some unambiguous expression for ordinary moments, moment generating function, incomplete moments, random number generator, mean deviation, entropies and order statistic are provided in this paper. We also discuss the estimation of parameters by using maximum likelihood estimation method. Finally, two real life applications are also provided to observe the flexibility of observed model as compared to some existing models.

The odd flexible Weibull-H family of distributions: Properties and estimation with applications to complete and upper record data

In this paper, a new generator of continuous distributions called the odd flexible Weibull-H family is proposed and studied. Some of its statistical properties including quantile, skewness, kurtosis, hazard rate function, moments, incomplete moments, mean deviations, coefficient of variation, Bonferroni and Lorenz curves, moments of the residual (past) lifetimes and entropies are studied. Two special models are introduced and discussed in-detail. The maximum likelihood method is used to estimate the model parameters based on complete and upper record data. Adetailed simulation study is carried out to examine the bias and mean square error of maximum likelihood estimators. Finally, three applications to real data sets show the flexibility of the new family.

On the Alpha Power Transformed Power Lindley Distribution

In this paper, we introduce a new generalization of the power Lindley distribution referred to asthe alpha power transformed power Lindley(APTPL). The APTPL model provides a better fit than the power Lindley distribution. It includes the alpha power transformed Lindley, power Lindley, Lindley, and gamma as special submodels. Various properties of the APTPL distribution including moments, incomplete moments, quantiles, entropy, and stochastic ordering are obtained. Maximum likelihood, maximum products of spacings, and ordinary and weighted least squares methods of estimation are utilized to obtain the estimators of the population parameters. Extensive numerical simulation is performed to examine and compare the performance of different estimates. Two important data sets are employed to show how the proposed model works in practice.

The Generalized Odd Lindley-G Family: Properties and Applications.

We introduce a new class of continuous distributions called the generalized odd Lindley-G family. Four special models of the new family are provided. Some explicit expressions for the quantile and generating functions, ordinary and incomplete moments, order statistics and Rényi and Shannon entropies are derived. The maximum likelihood method is used for estimating the model parameters. The flexibility of the generated family is illustrated by means of two applications to real data sets.

The Log-Odd Normal Generalized Family of Distributions with Application.

The normal distribution has a central place in distribution theory and statistics. We propose the log-odd normal generalized (LONG) family of distributions based on log-odds and obtain some of its mathematical properties including a useful linear representation for the new family. We investigate, as a special model, the log-odd normal power-Cauchy (LONPC) distribution. Some structural properties of LONPC distribution are obtained including quantile function, ordinary and incomplete moments, generating function and some asymptotics. We estimate the model parameters using the maximum likelihood method. The usefulness of the proposed family is proved empirically by means of a real air pollution data set.

The Exponentiated Kumaraswamy-G Class: General Properties and Application

We propose a new family of distributions called the exponentiated Kumaraswamy-G class with three extra positive parameters, which generalizes the Cordeiro and de Castro's family. Some special distributions in the new class are discussed. We derive some mathematical properties of the proposed class including explicit expressions for the quantile function, ordinary and incomplete moments, generating function, mean deviations, reliability, Rényi entropy and Shannon entropy. The method of maximum likelihood is used to fit the distributions in the proposed class. Simulations are performed in order to assess the asymptotic behavior of the maximum likelihood estimates. We illustrate its potentiality with applications to two real data sets which show that the extended Weibull model in the new class provides a better fit than other generalized Weibull distributions.

The Marshall-Olkin Generalized-G Family of Distributions with Applications

We introduce a new class of distributions called the Marshall-Olkin generalized-G family. Some of its mathematical properties including explicit expressions for the ordinary and incomplete moments, order statistics are discussed. The maximum likelihood method is used for estimating the model parameters. The importance and flexibility of the new family are illustrated by means of two applications to real data sets.

The Exponentiated Burr XII Power Series Distribution: Properties and Applications

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.

The Modified Beta Gompertz Distribution: Theory and Applications

In this paper, we introduce a new continuous probability distribution with five parameters called the modified beta Gompertz distribution. It is derived from the modified beta generator proposed by Nadarajah, Teimouri and Shih (2014) and the Gompertz distribution. By investigating its mathematical and practical aspects, we prove that it is quite flexible and can be used effectively in modeling a wide variety of real phenomena. Among others, we provide useful expansions of crucial functions, quantile function, moments, incomplete moments, moment generating function, entropies and order statistics. We explore the estimation of the model parameters by the obtained maximum likelihood method. We also present a simulation study testing the validity of maximum likelihood estimators. Finally, we illustrate the flexibility of the distribution by the consideration of two real datasets.

Logarithm Transformed Fr´echet Distribution : Properties and Estimation

In this paper, a new three-parameter distribution called the Alpha Logarithm Transformed Fr\'{e}chet (ALTF) distribution is introduced which offers a more flexible distribution for modeling lifetime data. Various properties of the proposed distribution, including explicit expressions for the quantiles, moments, incomplete moments, conditional moments, moment generating function R\'{e}nyi and $\delta$-entropies, stochastic ordering, stress-strength reliability and order statistics are derived. The new distribution can have decreasing, reversed J-shaped and upside-down bathtub failure rate functions depending on its parameter values. The maximum likelihood method is used to estimate the distribution parameters. A simulation study is conducted to evaluate the performance of the maximum likelihood estimates. Finally, the proposed extended model is applied on real data sets and the results are given which illustrate the superior performance of the ALTF distribution compared to some other well-known distributions.