Double Weighted Inverse Weibull Distribution (original) (raw)

On the Generalized Inverse Weibull Distribution

AIP Conference Proceedings, 2019

A new class of continuous distributions based on generalized inverse Weibull has been introduced. As a special case, generalized inverse Weibull-generalized inverse Weibull distribution is proposed. The probability density function, cumulative distribution function, reliability and hazard rate functions are introduced. Furthermore, most important statistical properties of the proposed distribution such as Shannon entropy, relative entropy, stress-strength model have been obtained.

The Weighted Inverse Weibull Distribution

International Journal of Research and Innovation in Applied Science

This paper introduces the Weighted Inverse Weibull distribution as inverse weighting of the Inverse Weibull distribution. Its various basic statistical properties were explicitly derived and the method of maximum likelihood estimation was used in estimating the model parameters. The model was applied to two real life data sets and its performance and flexibility was assessed with respect to existing distribution using the log-likelihood and Akaike Information Criteria as basis for judgment.

Generalized Modified Inverse Weibull Distribution: Its Properties and Applications

Sankhya B, 2019

In this paper, we introduce a new useful continuous distribution called generalized modified inverse Weibull distribution. This distribution is a fourparameter extension of the modified inverse Weibull which generalizes some well-known distributions. Various statistical and probabilistic properties are derived such as r th moment, moment generating function, Renyi and Shannon entropies and hazard rate function. We also discuss estimation of the parameters by maximum likelihood and provide the information matrix. The likelihood ratio order (which implies the hazard rate and usual stochastic orders) between smallest order statistics from two independent heterogeneous samples of this new family are discussed. Finally, a real numerical example is also considered for illustrative purposes.

Modified Inverse Weibull Distribution

A generalized version of four parameter modified inverse weibull distribution (MIWD) is introduced in this paper. This distribution generalizes the following distributions: (1) Modified Inverse exponential distribution, (2) Modified Inverse Rayleigh distribution, (3) Inverse weibull distribution. We provide a comprehensive description of the mathematical properties of the modified inverse weibull distribution along with its reliability behaviour. We derive the moments, moment generating function and examine the order statistics. We propose the method of maximum likelihood for estimating the model parameters and obtain the observed information matrix.

A New Generalized Weighted Weibull Distribution

Pakistan Journal of Statistics and Operation Research

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.

A Class of Weighted Weibull Distribution

SSRN Electronic Journal, 2000

The weighted Weibull model is proposed following the method of Azzalini (1985). Basic properties of the distribution including moments, generating function, hazard rate function and estimation of parameters have been studied.

Double Weighted Weibull Distribution Properties and Application

Mathematical theory and modeling, 2016

This paper offering a new weighted distribution known as the Double Weighted Weibull Distribution (DWWD). The statistical properties of the (DWWD) are derived and discussed, including the mean, variance, coefficient of variation, moments, mode, reliability function, hazard function and the reverse hazard function. Also the parameters of this distribution are estimated by the maximum likelihood estimation method . The plots of survival function, hazard function and reverse hazard function of (DWWD) are also presented. The worth of the distribution has been demonstrated by applying it to real life data. Keywords: Weighted distribution, Double Weighted distribution, Weibull distribution, Reliability estimation.

The Generalized Inverse Generalized Weibull Distribution and Its Properties

Journal of Probability, 2014

ABSTRACT The Inverse Weibull distribution has been applied to a wide range of situations including applications in medicine, reliability, and ecology. It can also be used to describe the degradation phenomenon of mechanical components. We introduce Inverse Generalized Weibull and Generalized Inverse Generalized Weibull (GIGW) distributions. GIGW distribution is a generalization of several distributions in literature. The mathematical properties of this distribution have been studied and the mixture model of two Generalized Inverse Generalized Weibull distributions is investigated. Estimates of parameters using method of maximum likelihood have been computed through simulations for complete and censored data.

Some Theoretical and Computational Aspects of the Inverse Generalized Power Weibull Distribution

Journal of Data Science, 2019

This paper introduces a new three-parameter distribution called inverse generalized power Weibull distribution. This distribution can be regarded as a reciprocal of the generalized power Weibull distribution. The new distribution is characterized by being a general formula for some well-known distributions, namely inverse Weibull, inverse exponential, inverse Rayleigh and inverse Nadarajah-Haghighi distributions. Some of the mathematical properties of the new distribution including the quantile, density, cumulative distribution functions, moments, moments generating function and order statistics are derived. The model parameters are estimated using the maximum likelihood method. The Monte Carlo simulation study is used to assess the performance of the maximum likelihood estimators in terms of mean squared errors. Two real datasets are used to demonstrate the flexibility of the new distribution as well as to demonstrate its applicability.

An extended version of Kumaraswamy inverse Weibull distribution and its properties

Statistica, 2016

Here we consider an extended version of the Kumaraswamy modified inverse Weibull distribution and investigate some of its theoretical properties through deriving expressions for cumulative distribution function, reliability function, hazard rate function, quantile function, characteristic function, raw moments, median, mode etc. Certain reliability measures of the distribution are obtained along with the distribution and moments of its order statistics. The maximum likelihood estimation of the parameters of the distribution is discussed and certain real life data applications are given for illustrating the usefulness of the model. Further, with the help of simulated data sets it is shown that the average bias and mean square errors of the maximum likelihood estimators are in decreasing order as the sample size increases.

The New Generalization of Weibull Distribution

2016

The Lomax-Weibull distribution is introduced as a new generalization of Weibull distribution. Some properties of the new distribution are investigated. Also, maximum likelihood and Bayesian estimation of the four unknown parameters are discussed. The asymptotic variancecovariance matrix is obtained. Finally, a numerical example is provided.

A New Expansion of the Inverse Weibull distribution: Properties with Applications

Iraqi Statisticians Journal, 2024

The use of statistical distributions to model life phenomena has received a great deal of attention in various sciences. Recent studies have shown the possibility of statistical distributions in data modeling in applied sciences, especially in environmental sciences. Among them is the inverse Weibull distribution, which is one of the most common statistical models that can be used very effectively in modeling data in the health, engineering, and environmental fields, as well as other fields. This study proposes to present a new generalization for the inverse Weibull distribution, where two new parameters are added to the basic distribution according to the Odd Lomax-G family so that the new generalization is more modern and flexible with real-world data. It is called the Odd Lomax Inverse Weibull (LoIW) distribution. The OLIW distribution comes with an expansion of its pdf and CDF functions by using binomial series, exponential, and Logarithm expansions with many statistical properties such as (Rényi entropy, moments, skewness, kurtosis with the moments generating function (mgf), ordered statistics, as well as the Quantile function), and the four distribution parameters are estimated using the maximum likelihood function (MLEs). To ensure the robustness of the proposed model, a practical application is conducted using the R language on two different types of real data and compared with many other statistical models.

On Three Parameter Discrete Generalized Inverse Weibull Distribution: Properties and Applications

Annals of Data Science, 2018

In this paper, a new discrete version of generalized inverse Weibull distribution is proposed using the general approach of discretization. Structural properties of the newly introduced discrete model have been discussed comprehensively. Characterization results have also been made to establish a direct link between the discrete generalized inverse Weibull distribution and its continuous counterpart. Various theorems relating a generalized inverse Weibull distribution with other probability models have also been proved. Finally, a real life count data set from medical sciences is used to illustrate the application of discrete inverse Weibull distribution. Keywords Discrete generalized inverse Weibull distribution • Medical sciences • Count data • Monte Carlo simulation • Index of dispersion

A new generalization of Weibull distribution

International Journal of Contemporary Mathematical Sciences, 2018

A NEW CLASS OF TRANSMUTED MODIFIED WEIGHTED WEIBULL DISTRIBUTION AND ITS PROPERTIES

Advances in Mathematics: Scientific Journal, 2021

An additional parameter was added to Modified Weighted Weibull distribution with method of quadratic rank transmutation which led to a newly developed distribution called Transmuted Modified Weighted Weibull distribution. Two distributions that emanated from the new distribution are Transmuted Modified Rayleigh and Transmuted Modified Exponential distributions. Some properties of the distribution that were obtained include; the survival rate, hazard rate, reverse hazard rate function; and moment generating function, mean and variance. Also, parameters of the model were estimated using maximum likelihood estimation method. The model was applied to a life time data set of total milk production of the first birth of 107 cows which showed a better performance compared to some existing known distributions.

The generalized inverse Weibull distribution

Statistical Papers, 2011

The inverse Weibull distribution has the ability to model failure rates which are quite common in reliability and biological studies. A three-parameter generalized inverse Weibull distribution with decreasing and unimodal failure rate is introduced and studied. We provide a comprehensive treatment of the mathematical properties of the new distribution including expressions for the moment generating function and the rth generalized moment. The mixture model of two generalized inverse Weibull distributions is investigated. The identifiability property of the mixture model is demonstrated. For the first time, we propose a location-scale regression model based on the log-generalized inverse Weibull distribution for modeling lifetime data. In addition, we develop some diagnostic tools for sensitivity analysis. Two applications of real data are given to illustrate the potentiality of the proposed regression model.

Skew-Generalized Inverse Weibull Distribution and Its Properties

2016

The skew-generalized inverse weibull distribution (SGIW) has four parameters of lifetime distribution. It could have different hazard rates: increasing, decreasing and unimodal. In this paper, the method of Azzalini's (1985) is used to provide a shape of parameter to generalize inverse weibull, which creates a new class of skew-generalized inverse weibull distributions. Different statistical properties of this new distribution are discussed whereas expressions for density, minimum and maximum order statistic and i th moment of the order statistics and the inference of the old parameters and the skewness parameter are studied. In addition, Mont Carlo simulation method was carried out to investigate the properties of the estimations of the unknown parameters of SGIW. Furthermore, the flexibility of SGIW model is illustrated by means of two real data sets applications.

Reflected Generalized Beta of Generalized Inverse Weibull Distribution: definition and properties

In this paper we study a new broad class of distribution functions which is defined by means of reflected generalized beta distribution. This class includes that of Beta-generated distribution as a special case. In particular, we extend the Generalized Inverse Weibull distribution proposed by Gusm\~ao et al. [2011], in order to obtain the Reflected Generalized Beta of Generalized Inverse Weibull Distribution. For this new distribution, moments, entropy, order statistics and a reliability measure are derived. The link between the InverseWeibull and the Dagum distribution is generalized. Then the maximum likelihood estimators of the parameters are examined and the observed Fisher information matrix provided. Finally, the usefulness of the model is illustrated by means of an application to real data.

On The Applications of Transmuted Inverted Weibull Distribution

2017

In this paper, we introduce a new distribution called transmuted inverted Weibull distribution (TIWD).The new distribution was used in analyzing bathtub failure rates lifetime data.We consider the standard transmuted inverted Weibull distribution (TIWD) that generalizes the standard inverted Weibull distribution (IWD), the new distribution has two shape parameters. The moments, median, survival function, hazard function, maximum likelihood estimators, leastsquares estimators, fisher information matrix and asymptotic confidence intervals were obtained. A real data set is analyzed and it is observed that the (TIWD) distribution can provide a better fitting than (IWD) distribution.