Beta-Linear Failure Rate Distribution and its Applications

In this paper we propose a new lifetime model, called the odd generalized exponential linear failure rate distribution. Some statistical properties of the proposed distribution such as the moments, the quantiles, the median, and the mode are investigated. The method of maximum likelihood is used for estimating the model parameters. An applications to real data is carried out to illustrate that the new distribution is more flexible and effective than other popular distributions in modeling lifetime data.

IEEE Transactions on Reliability, 2015

The hazard-rate or failure-rate is used in reliability theory as a measure o f the reliability o f a component. It measures the failure rate at time, t, of those components that have not already failed before time, t. If failures are completely random, then the failure rate is constant. This corresponds to an exponential distribution o f time to failure. As components wear out we can expect the failure rate to increase. On the other hand, new components often have defects which reduce their lifetimes. As these components fail we may expect the failure rate to decrease because the remaining components are more robust. These factors often combine to give a U-shaped (or bath tub shaped) hazard-rate. In practice, there will be a maximum theoretical life for any component, but we are unlikely to observe any component surviving anywhere near this maximum. Therefore, bounded life distributions might be o f interest. The beta distribution can be U-shaped and we use this as a hazard-rate function rather than as a density. The use o f this distribution is illustrated by fitting it to data from a human life table.

Computational Statistics & Data Analysis, 2011

The two-parameter linear failure rate distribution has been used quite successfully to analyze lifetime data. Recently, a new three-parameter distribution, known as the generalized linear failure rate distribution has been introduced by exponentiating the linear failure rate distribution. The generalized linear failure rate distribution is a very flexible lifetime distribution, and the probability density function of the generalized linear failure rate distribution can take different shapes. Its hazard function also can be increasing, decreasing and bathtub shaped. The main aim of this paper is to introduce a bivariate generalized linear failure rate distribution, whose marginals are generalized linear failure rate distributions. It is obtained using the same approach as the Marshall-Olkin bivariate exponential distribution. Different properties of this new distribution are established. The bivariate generalized linear failure rate distribution has five parameters and the maximum likelihood estimators are obtained using the EM algorithm. A data set is analyzed for illustrative purposes. Finally, some generalizations to the multivariate case are proposed.

Annals of Statistical Theory and Applications, 2019

In this work, a new skewed distribution called the reduced beta skewed Laplace distribution was proposed using the T-R{Y} method. The T-R{Y} nomenclature is about the newest methods of generating families of probability distributions. This method is very important in survival analysis in that each generated distribution is considered as a weighted hazard function of the base random variable, R. Some structural properties of the proposed distribution were derived, such as expressions for its moments, moments of the order statistics, and so forth. The maximum likelihood estimation of the model parameters was discussed, and the observed information matrix was derived. The importance and usefulness of the proposed model were illustrated using a real data set on time to fail of electrical components. Results from the Monte-Carlo experiment are quite good in favour of the new distribution. The performance of the proposed distribution was compared with those of other known selected distributions based on the real-life dataset and the results showed a good performance of the new model relative to others. This new distribution will provide new opportunities for assessing reliability and survival data in medicine, health, finance, environment, military, and other areas.

Pakistan Journal of Statistics and Operation Research, 2014

We introduce in this paper a new six-parameters generalized version of the generalized linear failure rate (GLFR) distribution which is called McDonald Generalized Linear failure rate (McGLFR) distribution. The new distribution is quite flexible and can be used effectively in modeling survival data and reliability problems. It can have a constant, decreasing, increasing, and upside down bathtub-and bathtub shaped failure rate function depending on its parameters. It includes some well-known lifetime distributions as special sub-models. Some structural properties of the new distribution are studied. Expressions for the density, moment generating function, conditional moments, mean deviation, Bonferroni and Lorentz curves also are obtained. Moreover we discuss maximum likelihood estimation of the unknown parameters of the new model.

Computational Statistics & Data Analysis, 2008

A four parameter generalization of the Weibull distribution capable of modeling a bathtubshaped hazard rate function is defined and studied. The beauty and importance of this distribution lies in its ability to model monotone as well as non-monotone failure rates, which are quite common in lifetime problems and reliability. The new distribution has a number of well-known lifetime special sub-models, such as the Weibull, extreme value, exponentiated Weibull, generalized Rayleigh and modified Weibull distributions, among others. We derive two infinite sum representations for its moments. The density of the order statistics is obtained. The method of maximum likelihood is used for estimating the model parameters. Also, the observed information matrix is obtained. Two applications are presented to illustrate the proposed distribution.

FUDMA JOURNAL OF SCIENCES, 2020

A lifetime model called Transmuted Exponential-Weibull Distribution was proposed in this research. Several statistical properties were derived and presented in an explicit form. Maximum likelihood technique is employed for the estimation of model parameters, and a simulation study was performed to examine the behavior of various estimates under different sample sizes and initial parameter values. Through using real-life datasets, it was empirically shown that the new model provides sufficient fits relative to other existing models.

Biostatistics and Biometrics Open Access Journal, 2018

In this paper, we proposed a new distribution to lifetime data with two parameters, the proposed distribution have increasing, decreasing and unimodal failure rates function. Some mathematical properties of the new distribution, including hazard function, moments, Estimation of Reliability, distribution of the order statistics and observed information matrix were presented. To estimate the model parameters, the Maximum Likelihood Estimate (MLE) technique was utilized. Then, one real data set were applied to show the significance and flexibility of the new distribution.

Communications in Statistics - Theory and Methods, 2002

In this paper, a new five-parameter generalized version of the Gompertz-Mekaham distribution called Beta Gompertz-Mekaham (BGM) distribution is being introduced. It includes some well-known lifetime distributions as special sub-models. The new distribution is quite flexible and can have a decreasing, increasing, and bathtub-shaped failure rate function depending on its parameters making it effective in modeling survival data and reliability problems. Some comprehensive properties of the new distribution, such as closed-form expressions for the density, cumulative distribution, hazard rate function, the rth order moment, moment are provided. The maximum likelihood estimation of the BGM parameters as well as observed Fisher's information matrix obtained. At the end, in order to show the capability of BMG over its sub models, an application to a real dataset illustrates its potentiality.

Journal of data science, 2021

A new class of distributions called the beta linear failure rate power series (BLFRPS) distributions is introduced and discussed. This class of distributions contains new and existing sub-classes of distributions including the beta exponential power series (BEPS) distribution, beta Rayleigh power series (BRPS) distribution, generalized linear failure rate power series (GLFRPS) distribution, generalized Rayleigh power series (GRPS) distribution, generalized exponential power series (GEPS) distribution, Rayleigh power series (RPS) distributions, exponential power series (EPS) distributions, and linear failure rate power series (LFRPS) distribution of Mahmoudi and Jafari (2014). The special cases of the BLFRPS distribution include the beta linear failure rate Poisson (BLFRP) distribution, beta linear failure rate geometric (BLFRG) distribution of Oluyede, Elbatal and Huang (2014), beta linear failure rate binomial (BLFRB) distribution, and beta linear failure rate logarithmic (BLFRL) d...

Communications in Statistics - Simulation and Computation

The linear exponential distribution is a generalization of the exponential and Rayleigh distributions. This distribution is one of the best models to fit data with increasing failure rate (IFR). But it does not provide a reasonable fit for modeling data with decreasing failure rate (DFR) and bathtub shaped failure rate (BTFR). To overcome this drawback, we propose a new record-based transmuted generalized linear exponential (RTGLE) distribution by using the technique of Balakrishnan and He (2021). The family of RTGLE distributions is more flexible to fit the data sets with IFR, DFR, and BTFR, and also generalizes several well-known models as well as some new record-based transmuted models. This paper aims to study the statistical properties of RTGLE distribution, like, the shape of the probability density function and hazard function, quantile function and its applications, moments and its generating function, order and record statistics, Rényi entropy. The maximum likelihood estimators, least squares and weighted least squares estimators, Anderson-Darling estimators, Cramér-von Mises estimators of the unknown parameters are constructed and their biases and mean squared errors are reported via Monte Carlo simulation study. Finally, the real data set based on failure time illustrates the goodness of fit and applicability of the proposed distribution; hence, suitable recommendations are forwarded.

Processes, 2022

Probability distributions perform a very significant role in the field of applied sciences, particularly in the field of reliability engineering. Engineering data sets are either negatively or positively skewed and/or symmetrical. Therefore, a flexible distribution is required that can handle such data sets. In this paper, we propose a new family of lifetime distributions to model the aforementioned data sets. This proposed family is known as a "New Modified Exponent Power Alpha Family of distributions" or in short NMEPA. The proposed family is obtained by applying the well-known T-X approach together with the exponential distribution. A three-parameter-specific submodel of the proposed method termed a "new Modified Exponent Power Alpha Weibull distribution" (NMEPA-Wei for short), is discussed in detail. The various mathematical properties including hazard rate function, ordinary moments, moment generating function, and order statistics are also discussed. In addition, we adopted the method of maximum likelihood estimation (MLE) for estimating the unknown model parameters. A brief Monte Carlo simulation study is conducted to evaluate the performance of the MLE based on bias and mean square errors. A comprehensive study is also provided to assess the proposed family of distributions by analyzing two real-life data sets from reliability engineering. The analytical goodness of fit measures of the proposed distribution are compared with well-known distributions including (i) APT-Wei (alpha power transformed Weibull), (ii) Ex-Wei (exponentiated-Weibull), (iii) classical two-parameter Weibull, (iv) Mod-Wei (modified Weibull), and (v) Kumar-Wei (Kumaraswamy-Weibull) distributions. The proposed class of distributions is expected to produce many more new distributions for fitting monotonic and non-monotonic data in the field of reliability analysis and survival analysis.

Mathematical Sciences

Bathtub failure rate shape is widely used in industrial and medical applications. In this paper, a three-parameter lifetime distribution, so-called the generalized Weibull uniform distribution that extends the Weibull distribution, is proposed and studied. This distribution has bathtub-shaped or decreasing failure rate function which enables it to fit real lifetime data sets. Various structural properties of the new distribution are derived, including explicit expressions for the quantile function, moments, moment-generating function and order statistics. Parameter estimations are provided by a maximum likelihood estimation, and the performance of the maximum likelihood estimation is evaluated using a simulation study. An application to real-life data demonstrates that the proposed distribution can be very useful in fitting real data.

The purpose of this paper is to introduce a new family of the quadratic hazard rate distribution. This new family has the advantage of being capable of modeling various shapes of aging and failure criteria. Furthermore, some well-known lifetime distributions such as generalized exponential distribution, generalized linear hazard rate distribution, and generalized Rayleigh distribution among others follow as special cases. Some statistical and reliability properties of the new family are discussed and the maximum likelihood estimation is used to estimate the unknown parameters. Explicit expressions are derived for the quantiles. In addition, the asymptotic confidence intervals for the parameters are derived from the Fisher information matrix. Finally, the obtained results are validated using a real data set and it is shown that the new family provides a better fit than some other known distributions.