A lifetime model with increasing failure rate (original) (raw)

Computational Statistics and Data Analysis The Poisson-exponential lifetime distribution

In this paper we proposed a new two-parameters lifetime distribution with increasing failure rate. The new distribution arises on a latent complementary risk problem base. The properties of the proposed distribution are discussed, including a formal proof of its probability density function and explicit algebraic formulae for its reliability and failure rate functions, quantiles and moments, including the mean and variance. A simple EM-type algorithm for iteratively computing maximum likelihood estimates is presented. The Fisher information matrix is derived analytically in order to obtaining the asymptotic covariance matrix. The methodology is illustrated on a real data set.

The Adjusted Log-logistic Generalized Exponential Distribution with Application to Lifetime Data

International Journal of Statistics and Probability

This paper introduces a new generator of probability distribution-the adjusted log-logistic generalized (ALLoG) distribution and a new extension of the standard one parameter exponential distribution called the adjusted log-logistic generalized exponential (ALLoGExp) distribution. The ALLoGExp distribution is a special case of the ALLoG distribution and we have provided some of its statistical and reliability properties. Notably, the failure rate could be monotonically decreasing, increasing or upside-down bathtub shaped depending on the value of the parameters delta\deltadelta and theta\thetatheta. The method of maximum likelihood estimation was proposed to estimate the model parameters. The importance and flexibility of he ALLoGExp distribution was demonstrated with a real and uncensored lifetime data set and its fit was compared with five other exponential related distributions. The results obtained from the model fittings shows that the ALLoGExp distribution provides a reasonably better fit tha...

A new lifetime model with decreasing failure rate

2010

In this paper we introduce a new lifetime distribution by compounding exponential and Poisson-Lindley distributions, named exponential Poisson-Lindley distribution. Several properties are derived, such as density, failure rate, mean lifetime, moments, order statistics and R\'enyi entropy. Furthermore, estimation by maximum likelihood and inference for large sample are discussed. The paper is motivated by two applications to real data sets and we hope that this model be able to attract wider applicability in survival and reliability.

A lifetime distribution with decreasing failure rate

Statistics & Probability Letters, 1998

A two-parameter distribution with decreasing failure rate is introduced. Various properties are discussed and the estimation of parameters is studied by the method of maximum likelihood. The estimates are attained by the EM algorithm and expressions for their asymptotic variances and covariances are obtained. Numerical examples based on real data are presented. ~)

Generalized Linear Failure Rate Distribution

Communications in Statistics - Theory and Methods, 2009

The exponential and Rayleigh are the two most commonly used distributions for analyzing lifetime data. These distributions have several desirable properties and nice physical interpretations. Unfortunately the exponential distribution only has constant failure rate and the Rayleigh distribution has increasing failure rate. The linear failure rate distribution generalizes both these distributions which may have non-increasing hazard function also. This paper introduces a new distribution, which generalizes the well known (1) exponential distribution, (2) linear failure rate distribution, (3) generalized exponential distribution, and (4) generalized Rayleigh distribution. The properties of this distribution are discussed in this paper. The maximum likelihood estimates of the unknown parameters are obtained. A real data set is analyzed and it is observed that the present distribution can provide a better fit than some other very well known distributions.

A New Two-Parameter Lifetime Distribution with Application

2020

There are several methods to combine and extend the continuous lifetime models to increase their flexibility and generality. Here we proposed a new lifetime distribution model with two parameters. Various lifetime distribution representations related to this model are derived and presented with their properties. Several Statistical measures and their properties are also studied. The method maximum likelihood estimator is discussed. Simulation studies are performed to assess the finite sample performance of the maximum likelihood estimators (MLEs) of the parameters. In the end, to show the flexibility of this distribution, an application using real data sets is presented

The Odd Generalized Exponential Linear Failure Rate Distribution

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.

A New Extension of the Exponential Power Distribution with Application to Lifetime Data

International Journal of Computational and Theoretical Statistics, 2018

This paper derives a new four-parameter generalized exponential power lifetime probability model for life time data, which generalizes some well-known exponential power lifetime distributions. It is observed that our proposed new distribution bears most of the properties of skewed distributions in reliability and life testing context. It is skewed to the right as well as its failure rate function has the increasing and bathtub shape behaviors. The estimation of the parameters, and simulation and applications of the proposed model have also been discussed.

The Generalized Exponential Distribution As a Lifetime Model under Different Loss Functions

Data Science Journal, 2009

Bayes estimates of the unknown parameter and the reliability function for the generalized exponential model are derived. Bayes estimates are obtained under various losses such as the squared error, the absolute error, the squared log error, and the entropy loss functions. Monte Carlo simulations are presented to compare the Bayes estimates and the maximum likelihood estimates of the unknown parameter and the reliability function.

A New Distribution with two parameters to Lifetime Data

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.