A Two-Parameter Pranav Distribution with Properties and Its Application.

2019 ◽  
Author(s):  
Edith Umeh ◽  
Amuche Ibenegbu
Keyword(s):  
Goodness Of Fit ◽  
Residual Life ◽  
Real Life ◽  
Lifetime Distribution ◽  
Mean Deviation ◽  
Mean Residual Life ◽  
Exponential Distributions ◽  
Hypertensive Patients ◽  
Study Results ◽  
Two Parameter

Introduction: Lifetime distribution has drawn so much attention in recent research, and this has lead to the development of new lifetime distribution. Addition of parameters to the existing distribution makes the distribution more flexible and reliable and applicable model has become the focus of the recent search. This paper proposed a two-parameter Pranav distribution which has its base from a one-parameter Pranav and Ishita distribution. Methods Two parameter Pranav distribution was proposed. Mathematical and statistical properties of the distribution which includes; moments, coefficient of variation, skewness, kurtosis, index of dispersion, hazard rate function, mean residual life function, stochastic ordering, mean deviation, Bonferroni and Lorenz curves were developed. Other lifetime distributions such as Ishita, Akash, Sujatha, Shanker, Lindley, and Exponential distributions were considered in the study. Results: This new distribution was compared with two-parameter Akash, Lindley, one parameter Pranav, Ishita, Akash, Sujatha, Shanker, Lindley, and Exponential distributions to determine the efficiency of the new model. The estimation of parameters has been X-rayed using the method of moments and maximum likelihood. Also, AIC and BIC were used to test for the goodness of fit of the model which was applied to a real-life data of hypertensive patients. The results show that the new two-parameter Pranav distribution has the lowest value of AIC and BIC Conclusion: Based on the AIC and BIC values we can conclude that the two-parameter Pranav is more efficient than the other distribution for modeling survival of hypertensive patients. Hence two-parameter Pranav can be seen as an important distribution in modeling lifetime data.

scholarly journals A Two-parameter Rama Distribution

2019 ◽  
pp. 365-382
Author(s):  
U. Umeh Edith ◽  
T. Umeokeke Ebele ◽  
A. Ibenegbu Henrietta
Keyword(s):  
Goodness Of Fit ◽  
Residual Life ◽  
Real Life ◽  
Stochastic Ordering ◽  
Rate Function ◽  
Mean Deviation ◽  
Mean Residual Life ◽  
Estimation Of Parameters ◽  
Lorenz Curves ◽  
Two Parameter

In this paper, a two-parameter Rama distribution is proposed. This is coined from Lindley distribution and Rama distribution. Its mathematical and statistical properties which include its shapes, moment, coefficient of variation, skewness, kurtosis, index of dispersion, hazard rate function, mean residual life function, stochastic ordering, mean deviation; Bonferroni and Lorenz curves are also discussed. The estimation of parameters has been X-rayed using methods of moment and maximum likelihood. Also AIC and BIC are used to test for the goodness of fit of the model which is applied to a real life data of hepatitis B patients. This new distribution is compared with Rama, 2-parameter Akash, 2-parameter Lindley, Akash, Shanker, Ishita, Lindley and Exponential distributions in order to determine the efficiency of the new model.

A FINITE RANGE DISCRETE LIFE DISTRIBUTION

1995 ◽  
Vol 02 (02) ◽  
pp. 147-160 ◽  
Author(s):  
C.D. LAI ◽  
D.Q. WANG
Keyword(s):  
Failure Time ◽  
Residual Life ◽  
Discrete Distribution ◽  
Lifetime Distribution ◽  
Mortality Data ◽  
Mean Residual Life ◽  
Life Distribution ◽  
Life Data ◽  
Proposed Model ◽  
Two Parameter

Discrete life data arise in many practical situations and even for continuous data we may find cases where the data are presented in grouped form, so that a discrete model can be used. In this paper, we propose a new two-parameter discrete lifetime distribution for modeling this type of data. The distribution under consideration has some interesting ageing properties; in particular, it is able to describe bathtub-shaped failure rate as well as upside-down bathtub-shaped mean residual life. We use this discrete distribution to model Halley’s mortality data and find it fits reasonably well. The proposed model, though quite simple in appearance, is flexible and potentially useful in describing various types of failure time. Some analytical results will also be presented.

scholarly journals Odoma Distribution and Its Application

2019 ◽  
pp. 1-11
Author(s):  
C. C. Odom ◽  
M. A. Ijomah
Keyword(s):  
Goodness Of Fit ◽  
Residual Life ◽  
Survival Function ◽  
Real Life ◽  
Rate Function ◽  
Mean Residual Life ◽  
Mathematical Properties ◽  
Real Life Data ◽  
Method Of Maximum Likelihood ◽  
New Distribution

In this study, a new continuous one parameter lifetime distribution is proposed. Its mathematical properties such as moments, order statistics, entropy, survival function, hazard rate function and mean residual life function are derived. The new distribution is applied to real-life data from engineering and the method of maximum likelihood is used to estimate the parameter. The goodness-of-fit of the new distribution shows its better fit to the data than some competing distributions.

scholarly journals A GENERALIZATION OF SUJATHA DISTRIBUTION AND ITS APPLICATIONS WITH REAL LIFETIME DATA

2017 ◽  
Vol 22 (1) ◽  
pp. 66-83 ◽  
Author(s):  
Rama Shanker ◽  
Kamlesh Kumar Shukla ◽  
Hagos Fesshaye
Keyword(s):  
Residual Life ◽  
Estimation Method ◽  
Likelihood Estimation ◽  
Stochastic Ordering ◽  
Rate Function ◽  
Mean Residual Life ◽  
Exponential Distributions ◽  
Lorenz Curves ◽  
Two Parameter ◽  
Life Function

A two-parameter generalization of Sujatha distribution (AGSD), which includes Lindley distribution and Sujatha distribution as particular cases, has been proposed. It's important mathematical and statistical properties including its shape for varying values of parameters, moments, coefficient of variation, skewness, kurtosis, index of dispersion, hazard rate function, mean residual life function, stochastic ordering, mean deviations, Bonferroni and Lorenz curves, and stress-strength reliability have been discussed. Maximum likelihood estimation method has been discussed for estimating its parameters. AGSD provides better fit than Sujatha, Aradhana, Lindley and exponential distributions for modeling real lifetime data.Journal of Institute of Science and TechnologyVolume 22, Issue 1, July 2017, Page: 66-83

A new two-parameter lifetime distribution with flexible hazard rate function: Properties, applications and different method of estimations

2021 ◽  
Vol 71 (4) ◽  
pp. 983-1004
Author(s):  
Majid Hashempour
Keyword(s):  
Residual Life ◽  
Real Data ◽  
Quantile Function ◽  
Rate Function ◽  
Lifetime Distribution ◽  
Maximum Likelihood Estimates ◽  
Residual Entropy ◽  
Mean Residual Life ◽  
Conditional Moments ◽  
Two Parameter

Abstract In this paper, we introduce a new two-parameter lifetime distribution which is called extended Half-Logistic (EHL) distribution. Theoretical properties of this model including the hazard function, quantile function, asymptotic, extreme value, moments, conditional moments, mean residual life, mean past lifetime, residual entropy, cumulative residual entropy and order statistics are derived and studied in details. The maximum likelihood estimates of parameters are compared with various methods of estimations by conducting a simulation study. Finally, two real data sets are illustration the purposes.

scholarly journals Two-Parameter Nwikpe (TPAN) Distribution with Application

2021 ◽  
pp. 56-67
Author(s):  
Barinaadaa John Nwikpe ◽  
Isaac Didi Essi
Keyword(s):  
Goodness Of Fit ◽  
Continuous Distribution ◽  
Real Life ◽  
Moment Generating Function ◽  
Statistical Properties ◽  
Likelihood Method ◽  
Data Sets ◽  
Method Of Moment ◽  
Two Parameter ◽  
New Distribution

A new two-parameter continuous distribution called the Two-Parameter Nwikpe (TPAN) distribution is derived in this paper. The new distribution is a mixture of gamma and exponential distributions. A few statistical properties of the new probability distribution have been derived. The shape of its density for different values of the parameters has also been established.  The first four crude moments, the second and third moments about the mean of the new distribution were derived using the method of moment generating function. Other statistical properties derived include; the distribution of order statistics, coefficient of variation and coefficient of skewness. The parameters of the new distribution were estimated using maximum likelihood method. The flexibility of the Two-Parameter Nwikpe (TPAN) distribution was shown by fitting the distribution to three real life data sets. The goodness of fit shows that the new distribution outperforms the one parameter exponential, Shanker and Amarendra distributions for the data sets used for this study.

PRESERVATION OF STOCHASTIC ORDERS UNDER MIXTURES OF EXPONENTIAL DISTRIBUTIONS

2006 ◽  
Vol 20 (4) ◽  
pp. 655-666 ◽  
Author(s):  
Jarosław Bartoszewicz ◽  
Magdalena Skolimowska
Keyword(s):  
Hazard Rate ◽  
Residual Life ◽  
Stochastic Order ◽  
Stochastic Orders ◽  
Mean Residual Life ◽  
Exponential Distributions ◽  
Dispersive Order ◽  
Mixing Distributions ◽  
Convex Transform Order ◽  
Star Order

Recently, Bartoszewicz [5,6] considered mixtures of exponential distributions treated as the Laplace transforms of mixing distributions and established some stochastic order relations between them: star order, dispersive order, dilation. In this article the preservation of the likelihood ratio, hazard rate, reversed hazard rate, mean residual life, and excess wealth orders under exponential mixtures is studied. Some new preservation results for the dispersive order are given, as well as the preservation of the convex transform order, and the star one is discussed.

scholarly journals The Kumaraswamy Pareto IV Distribution

2021 ◽  
Vol 50 (5) ◽  
pp. 1-22
Author(s):  
Muhammad Hussain Tahir ◽  
Gauss M. Cordeiro ◽  
Muhammad Mansoor ◽  
Muhammad Zubair ◽  
Ayman Alzaatreh
Keyword(s):  
Density Function ◽  
Residual Life ◽  
Information Matrix ◽  
Real Life ◽  
Quantile Function ◽  
Mean Residual Life ◽  
Model Parameters ◽  
New Model ◽  
Lorenz Curves ◽  
Mean Waiting Time

We introduce a new model named the Kumaraswamy Pareto IV distribution which extends the Pareto and Pareto IV distributions. The density function is very flexible and can be left-skewed, right-skewed and symmetrical shapes. It hasincreasing, decreasing, upside-down bathtub, bathtub, J and reversed-J shaped hazard rate shapes. Various structural properties are derived including explicit expressions for the quantile function, ordinary and incomplete moments,Bonferroni and Lorenz curves, mean deviations, mean residual life, mean waiting time, probability weighted moments and generating function. We provide the density function of the order statistics and their moments. The Renyi and q entropies are also obtained. The model parameters are estimated by the method of maximum likelihood and the observed information matrix is determined. The usefulness of the new model is illustrated by means of three real-life data sets. In fact, our proposed model provides a better fit to these data than the gamma-Pareto IV, gamma-Pareto, beta-Pareto,exponentiated Pareto and Pareto IV models.

ON BOUNDS AND APPROXIMATING WEIGHTED DISTRIBUTIONS BY EXPONENTIAL DISTRIBUTIONS

2006 ◽  
Vol 20 (3) ◽  
pp. 517-528 ◽  
Author(s):  
Broderick O. Oluyede
Keyword(s):  
Error Bounds ◽  
Hazard Rate ◽  
Residual Life ◽  
Weight Functions ◽  
Mean Residual Life ◽  
Exponential Distributions ◽  
Lifetime Distributions ◽  
Weighted Distributions

In this article, we obtain error bounds for exponential approximations to the classes of weighted residual and equilibrium lifetime distributions with monotone weight functions. These bounds are obtained for the class of distributions with increasing (decreasing) hazard rate and mean residual life functions.

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