scholarly journals A Generalized Family of Lifetime Distributions and Survival Models

2020 ◽  
Vol 18 (2) ◽  
pp. 2-34
Author(s):  
Mamoud Aldeni ◽  
Felix Famoye ◽  
Carl Lee
Keyword(s):  
Hazard Rate ◽  
Hazard Function ◽  
Lifetime Distribution ◽  
Survival Models ◽  
Data Sets ◽  
Lifetime Data ◽  
Data Set ◽  
Lifetime Distributions ◽  
Rate Functions ◽  
Common Technique

In lifetime data, the hazard function is a common technique for describing the characteristics of lifetime distribution. Monotone increasing or decreasing, and unimodal are relatively simple hazard function shapes, which can be modeled by many parametric lifetime distributions. However, fewer distributions are capable of modeling diverse and more complicated shapes such as N-shaped, reflected N-shaped, W-shaped, and M-shaped hazard rate functions. A generalized family of lifetime distributions, the uniform-R{generalized lambda} (U-R{GL}) are introduced and the corresponding survival models are derived, and applied to two lifetime data sets. The survival model is applied to a right censored lifetime data set.

scholarly journals Some classes of statistical distributions. Properties and Applications

2018 ◽  
Vol 26 (1) ◽  
pp. 43-68
Author(s):  
Irina Băncescu
Keyword(s):  
Statistical Models ◽  
Hazard Rate ◽  
Real Data ◽  
Data Sets ◽  
Statistical Distributions ◽  
Coherent Systems ◽  
Lifetime Distributions ◽  
Rate Functions ◽  
Series Systems ◽  
Parallel Series

Abstract We propose a new method of constructing statistical models which can be interpreted as the lifetime distributions of series-parallel/parallel- series systems used in characterizing coherent systems. An open problem regarding coherent systems is comparing the expected system lifetimes. Using these models, we discuss and establish conditions for ordering of expected system lifetimes of complex series-parallel/parallel-series systems. Also, we consider parameter estimation and the analysis of two real data sets. We give formulae for the reliability, hazard rate and mean hazard rate functions.

scholarly journals The Comparison Between Gumbel and Exponentiated Gumbel Distributions and Their Applications in Hydrological Process

2021 ◽  
Vol 2 (1) ◽  
Keyword(s):  
Hazard Rate ◽  
Gumbel Distribution ◽  
Real Data ◽  
Statistical Characteristics ◽  
Data Sets ◽  
Hydrological Process ◽  
Lifetime Data ◽  
Data Set ◽  
Method Of Maximum Likelihood ◽  
First Moment

The Exponentiated Gumbel (EG) distribution has been proposed to capture some aspects of the data that the Gumbel distribution fails to specify. it has an increasing hazard rate. The Exponentiated Gumbel distribution has applications in hydrology, meteorology, climatology, insurance, finance and geology, among many others. In this paper Firstly, the mathematical and statistical characteristics of the gumbel and Exponentiated Gumbel distribution are presented, then the applications of this distributions are studied using the real data set. Its first moment about origin and moments about mean have been obtained and expressions for skewness, kurtosis have been given. Estimation of its parameter has been discussed using the method of maximum likelihood. In the end, two applications of the gumbel and exponentiated gumbel distribution have been discussed with two real lifetime data sets. The results also confirmed the suitability of the Exponentiated Gumbel distribution for real data collection.

scholarly journals On Modified Burr XII-Inverse Weibull Distribution: Development, Properties, Characterizations and Applications

2020 ◽  
pp. 721-735
Author(s):  
Fiaz Ahmad Bhatti ◽  
G. G. Hamedani ◽  
Haitham M. Yousof ◽  
Azeem Ali ◽  
Munir Ahmad
Keyword(s):  
Maximum Likelihood ◽  
Hazard Rate ◽  
Maximum Likelihood Method ◽  
Real Data ◽  
Lifetime Distribution ◽  
Maximum Likelihood Estimates ◽  
Likelihood Method ◽  
Data Sets ◽  
Quarterly Earnings ◽  
Inverse Weibull Distribution

A flexible lifetime distribution with increasing, decreasing, inverted bathtub and modified bathtub hazard rate called Modified Burr XII-Inverse Weibull (MBXII-IW) is introduced and studied. The density function of MBXII-IW is exponential, left-skewed, right-skewed and symmetrical shaped.  Descriptive measures on the basis of quantiles, moments, order statistics and reliability measures are theoretically established. The MBXII-IW distribution is characterized via different techniques. Parameters of MBXII-IW distribution are estimated using maximum likelihood method. The simulation study is performed to illustrate the performance of the maximum likelihood estimates (MLEs). The potentiality of MBXII-IW distribution is demonstrated by its application to real data sets: serum-reversal times and quarterly earnings.

scholarly journals Extended Odd Fréchet-G Family of Distributions

2018 ◽  
Vol 2018 ◽  
pp. 1-12 ◽  
Author(s):  
Suleman Nasiru
Keyword(s):  
Maximum Likelihood Method ◽  
Real Data ◽  
Likelihood Method ◽  
Data Sets ◽  
Data Set ◽  
New Class ◽  
New Family ◽  
Rate Functions ◽  
The Given ◽  
Family Of Distributions

The need to develop generalizations of existing statistical distributions to make them more flexible in modeling real data sets is vital in parametric statistical modeling and inference. Thus, this study develops a new class of distributions called the extended odd Fréchet family of distributions for modifying existing standard distributions. Two special models named the extended odd Fréchet Nadarajah-Haghighi and extended odd Fréchet Weibull distributions are proposed using the developed family. The densities and the hazard rate functions of the two special distributions exhibit different kinds of monotonic and nonmonotonic shapes. The maximum likelihood method is used to develop estimators for the parameters of the new class of distributions. The application of the special distributions is illustrated by means of a real data set. The results revealed that the special distributions developed from the new family can provide reasonable parametric fit to the given data set compared to other existing distributions.

scholarly journals The Exponentiated Gumbel Type-2 Distribution: Properties and Application

2016 ◽  
Vol 2016 ◽  
pp. 1-10 ◽  
Author(s):  
I. E. Okorie ◽  
A. C. Akpanta ◽  
J. Ohakwe
Keyword(s):  
Lifetime Distribution ◽  
The Other ◽  
Maximum Likelihood Estimates ◽  
Model Parameters ◽  
Lifetime Data ◽  
Data Set ◽  
Method Of Maximum Likelihood ◽  
Log Likelihood ◽  
New Distribution

We introduce a generalized version of the standard Gumble type-2 distribution. The new lifetime distribution is called the Exponentiated Gumbel (EG) type-2 distribution. The EG type-2 distribution has three nested submodels, namely, the Gumbel type-2 distribution, the Exponentiated Fréchet (EF) distribution, and the Fréchet distribution. Some statistical and reliability properties of the new distribution were given and the method of maximum likelihood estimates was proposed for estimating the model parameters. The usefulness and flexibility of the Exponentiated Gumbel (EG) type-2 distribution were illustrated with a real lifetime data set. Results based on the log-likelihood and information statistics values showed that the EG type-2 distribution provides a better fit to the data than the other competing distributions. Also, the consistency of the parameters of the new distribution was demonstrated through a simulation study. The EG type-2 distribution is therefore recommended for effective modelling of lifetime data.

scholarly journals Statistical Properties of a New Bathtub Shaped Failure Rate Model With Applications in Survival and Failure Rate Data

2021 ◽  
Vol 10 (3) ◽  
pp. 49
Author(s):  
Muhammad Z. Arshad ◽  
Muhammad Z. Iqbal ◽  
Alya Al Mutairi
Keyword(s):  
Failure Rate ◽  
Quantile Function ◽  
Data Sets ◽  
Lifetime Data ◽  
Rate Data ◽  
Rate Model ◽  
Unknown Parameters ◽  
Method Of Maximum Likelihood ◽  
Rate Functions ◽  
Lifetime Model

In this study, we proposed a flexible lifetime model identified as the modified exponentiated Kumaraswamy (MEK) distribution. Some distributional and reliability properties were derived and discussed, including explicit expressions for the moments, quantile function, and order statistics. We discussed all the possible shapes of the density and the failure rate functions. We utilized the method of maximum likelihood to estimate the unknown parameters of the MEK distribution and executed a simulation study to assess the asymptotic behavior of the MLEs. Four suitable lifetime data sets we engaged and modeled, to disclose the usefulness and the dominance of the MEK distribution over its participant models.

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

2017 ◽  
Vol 5 (4) ◽  
pp. 1
Author(s):  
I. E. Okorie ◽  
A. C. Akpanta ◽  
J. Ohakwe ◽  
D. C. Chikezie ◽  
C. U. Onyemachi ◽  
...  
Keyword(s):  
Exponential Distribution ◽  
Likelihood Estimation ◽  
Model Parameters ◽  
Data Sets ◽  
Lifetime Data ◽  
Generalized Exponential Distribution ◽  
Data Set ◽  
Method Of Maximum Likelihood ◽  
The One ◽  
Special Case

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 $\delta$ and $\theta$. 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 than the one based on the other fitted distributions. The ALLoGExp distribution is therefore ecommended for effective modelling of lifetime data sets.

scholarly journals The complementary Poisson-Lindley class of distributions

2015 ◽  
Vol 3 (2) ◽  
pp. 146 ◽  
Author(s):  
Amal Hassan ◽  
Salwa Assar ◽  
Kareem Ali
Keyword(s):  
Information Matrix ◽  
Real Data ◽  
Formal Proof ◽  
Cumulative Distribution ◽  
Likelihood Method ◽  
Unknown Parameters ◽  
Data Set ◽  
Lifetime Distributions ◽  
New Class ◽  
Rate Functions

<p>This paper proposed a new general class of continuous lifetime distributions, which is a complementary to the Poisson-Lindley family proposed by Asgharzadeh et al. [3]. The new class is derived by compounding the maximum of a random number of independent and identically continuous distributed random variables, and Poisson-Lindley distribution. Several properties of the proposed class are discussed, including a formal proof of probability density, cumulative distribution, and reliability and hazard rate functions. The unknown parameters are estimated by the maximum likelihood method and the Fisher’s information matrix elements are determined. Some sub-models of this class are investigated and studied in some details. Finally, a real data set is analyzed to illustrate the performance of new distributions.</p>

Some Discrete Lifetime Distributions with Bathtub-Shaped Hazard Rate Functions

2013 ◽  
Vol 25 (3) ◽  
pp. 225-236 ◽  
Author(s):  
M. Shafaei Noughabi ◽  
A. H. Rezaei Roknabadi ◽  
G. R. Mohtashami Borzadaran
Keyword(s):  
Hazard Rate ◽  
Lifetime Distributions ◽  
Rate Functions

scholarly journals The Exponential-Generalized Truncated Geometric (EGTG) Distribution: A New Lifetime Distribution

2017 ◽  
Vol 7 (1) ◽  
pp. 1 ◽  
Author(s):  
Mohieddine Rahmouni ◽  
Ayman Orabi
Keyword(s):  
Probability Distribution ◽  
Real Data ◽  
Lifetime Distribution ◽  
Data Sets ◽  
Application Study ◽  
Maximum Lifetime ◽  
Special Cases ◽  
Rate Functions ◽  
Two Parameter ◽  
New Distribution

This paper introduces a new two-parameter lifetime distribution, called the exponential-generalized truncated geometric (EGTG) distribution, by compounding the exponential with the generalized truncated geometric distributions. The new distribution involves two important known distributions, i.e., the exponential-geometric (Adamidis and Loukas, 1998) and the extended (complementary) exponential-geometric distributions (Adamidis et al., 2005; Louzada et al., 2011) in the minimum and maximum lifetime cases, respectively. General forms of the probability distribution, the survival and the failure rate functions as well as their properties are presented for some special cases. The application study is illustrated based on two real data sets.

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