scholarly journals A Two Parameter Odd Exponentiated Skew-T Distribution With J-Shaped Hazard Rate Function

2021 ◽  
Vol 3 (1) ◽  
pp. 26-46
Author(s):  
O. D. Adubisi ◽  
A. Abdulkadir ◽  
H. Chiroma
Keyword(s):  
Hazard Rate ◽  
Real Life ◽  
Estimation Method ◽  
Likelihood Estimation ◽  
Quantile Function ◽  
Rate Function ◽  
Parameter Estimates ◽  
Finite Sample ◽  
T Distribution ◽  
Two Parameter

A new generalization of the skew-t distribution was proposed. The two-parameter lifetime model called the odd exponentiated skew-t distribution has the ability of fitting skewed, long and heavy tailed datasets. It is considered to be more flexible than the skew-t distribution as it contains it as a special case. Some basic properties of the distribution such as the order statistics, entropy, asymptotic behaviour, moment, incomplete moment, characteristic function and quantile function were derived. The odd exponentiated skew-t distribution parameter estimates were derived using the maximum likelihood estimation method and simulation studies performed to evaluate the finite sample performance of these parameter estimates showed that the parameter estimates were consistent and approached the arbitrary selected parameter values as the sample size is increased. The application using a real-life dataset indicated that the new distribution outperformed the other competing distributions. The hazard rate shape of the odd exponentiated skew-t distribution was found to be increasing and J-shaped which was also reflected in the application result.

scholarly journals Generalized Weibull–Lindley (GWL) Distribution in Modeling Lifetime Data

2020 ◽  
Vol 2020 ◽  
pp. 1-15
Author(s):  
Pius Marthin ◽  
Gadde Srinivasa Rao
Keyword(s):  
Survival Function ◽  
Real Life ◽  
Likelihood Estimation ◽  
Quantile Function ◽  
Rate Function ◽  
Parameter Estimates ◽  
Lifetime Data ◽  
Median Order ◽  
Probability Density Function Pdf ◽  
Two Parameter

In this manuscript, we have derived a new lifetime distribution named generalized Weibull–Lindley (GWL) distribution based on the T-X family of distribution specifically the generalized Weibull-X family of distribution. We derived and investigated the shapes of its probability density function (pdf), hazard rate function, and survival function. Some statistical properties such as quantile function, mode, median, order statistics, Shannon entropy, Galton skewness, and Moors kurtosis have been derived. Parameter estimation was done through maximum likelihood estimation (MLE) method. Monte Carlo simulation was conducted to check the performance of the parameter estimates. For the inference purpose, two real-life datasets were applied and generalized Weibull–Lindley (GWL) distribution appeared to be superior over its competitors including Lindley distribution, Akash distribution, new Weibull-F distribution, Weibull–Lindley (WL) distribution, and two-parameter Lindley (TPL) distribution.

scholarly journals The Zubair-dagum Distribution

2021 ◽  
pp. 25-35
Author(s):  
O. R. Uwaeme ◽  
N. P. Akpan
Keyword(s):  
Real Life ◽  
Estimation Method ◽  
Likelihood Estimation ◽  
Quantile Function ◽  
Moment Generating Function ◽  
Parameter Estimates ◽  
Mathematical Properties ◽  
Dagum Distribution ◽  
Maximum Likelihood Estimation Method ◽  
New Distribution

This article examines the flexibility of the Zubair-G family of distribution using the Dagum distribution. The proposed distribution is called the Zubair-Dagum distribution. The various mathematical properties of this distribution such as the Quantile function, Moments, Moment generating function, Reliability analysis, Entropy and Order statistics were obtained. The parameter estimates of the proposed distribution were also derived and estimated using the maximum likelihood estimation method. The new distribution is right skewed and has various bathtub and monotonically decreasing shapes. Our numerical illustrations using two real-life datasets substantiate the applicability, flexibility and superiority of the proposed distribution over competing distributions.

scholarly journals The Maxwell – Exponential Distribution: Theory and Application to Lifetime Data

2021 ◽  
Vol 3 (2) ◽  
pp. 65-80
Author(s):  
Usman Aliyu Abdullahi ◽  
Ahmad Abubakar Suleiman ◽  
Aliyu Ismail Ishaq ◽  
Abubakar Usman ◽  
Aminu Suleiman
Keyword(s):  
Exponential Distribution ◽  
Survival Function ◽  
Real Life ◽  
Estimation Method ◽  
Likelihood Estimation ◽  
Quantile Function ◽  
Information Criteria ◽  
Cumulative Distribution ◽  
Two Parameters ◽  
Maximum Likelihood Estimation Method

Two parameters Maxwell – Exponential distribution was proposed using the Maxwell generalized family of distribution. The probability density function, cumulative distribution function, survival function, hazard function, quantile function, and statistical properties of the proposed distribution are discussed. The parameters of the proposed distribution have been estimated using the maximum likelihood estimation method. The potentiality of the estimators was shown using a simulation study. The overall assessment of the performance of Maxwell - Exponential distribution was determined by using two real-life datasets. Our findings reveal that the Maxwell – Exponential distribution is more flexible compared to other competing distributions as it has the least value of information criteria.

scholarly journals A generalization to the log-inverse Weibull distribution and its applications in cancer research

2021 ◽  
Vol 8 (1) ◽  
Author(s):  
C. Satheesh Kumar ◽  
Subha R. Nair
Keyword(s):  
Maximum Likelihood ◽  
Weibull Distribution ◽  
Real Life ◽  
Simulated Data ◽  
Likelihood Estimation ◽  
Quantile Function ◽  
Reliability Function ◽  
Rate Function ◽  
Data Sets ◽  
Inverse Weibull Distribution

AbstractIn this paper we consider a generalization of a log-transformed version of the inverse Weibull distribution. Several theoretical properties of the distribution are studied in detail including expressions for its probability density function, reliability function, hazard rate function, quantile function, characteristic function, raw moments, percentile measures, entropy measures, median, mode etc. Certain structural properties of the distribution along with expressions for reliability measures as well as the distribution and moments of order statistics are obtained. Also we discuss the maximum likelihood estimation of the parameters of the proposed distribution and illustrate the usefulness of the model through real life examples. In addition, the asymptotic behaviour of the maximum likelihood estimators are examined with the help of simulated data sets.

scholarly journals The Type I Half Logistic Skew-t Distribution: A Heavy-Tail Model with Inverted Bathtub Shaped Hazard Rate

2021 ◽  
pp. 21-40
Author(s):  
O. D. Adubisi ◽  
A. Abdulkadir ◽  
H. Chiroma ◽  
U. F. Abbas
Keyword(s):  
Hazard Rate ◽  
Likelihood Method ◽  
Parameter Estimates ◽  
Type I ◽  
Long Tail ◽  
Student T Distribution ◽  
Heavy Tailed ◽  
T Distribution ◽  
Two Parameter ◽  
New Distribution

In this article a new generalization of the skew student-t distribution was introduced. The two-parameter model called the type I half-logistic skew-t (TIHLST) distribution can fit skewed, heavy-right tail, and long-tail datasets. Statistical properties of the type I half-logistic skew-t (TIHLST) distribution were derived and the maximum likelihood method parameter estimates assessed through a simulation study. A well-known dataset was analysed, illustrating the usefulness of the new distribution in modeling skewed and heavy-tailed data. The hazard rate shape was found to be increasing, decreasing and inverted bathtub shaped which was also reflected in the application result.

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

scholarly journals Pseudo-Lindley Family of Distributions and its Properties

2021 ◽  
pp. 35-49
Author(s):  
U. U. Uwadi ◽  
E. E. Nwezza
Keyword(s):  
Hazard Rate ◽  
Maximum Likelihood Method ◽  
Quantile Function ◽  
Rate Function ◽  
Likelihood Method ◽  
Parameter Estimates ◽  
New Family ◽  
The Family ◽  
Renyi’S Entropy ◽  
Family Of Distributions

In this study, we proposed a family of distribution called the Pseudo Lindley family of distributions. The limiting behaviors of the density and hazard rate function of the new family are examined. Statistical properties of the proposed family of distributions derived include quantile function, moments, order statistics, and Renyi’s entropy. The maximum likelihood method was employed in obtaining the parameter estimates of the Pseudo Lindley family of distribution. Bivariate extension of the proposed family is discussed. Some special members of the family are obtained. The shape of the density function of special members could be unimodal, bathtub shaped, increasing and decreasing. 

scholarly journals Exponentiated Frechet Distribution with Application in Temperature of Assam, India Overview with New Properties and Estimation

2021 ◽  
pp. 211-225
Author(s):  
Umme Habibah Rahman ◽  
Tanusree Deb Roy
Keyword(s):  
Hazard Rate ◽  
Goodness Of Fit ◽  
Survival Function ◽  
Information Matrix ◽  
Estimation Method ◽  
Likelihood Estimation ◽  
Rate Function ◽  
Hazard Rate Function ◽  
Fréchet Distribution ◽  
Frechet Distribution

In this paper, a new kind of distribution has suggested with the concept of exponentiate. The reliability analysis including survival function, hazard rate function, reverse hazard rate function and mills ratio has been studied here. Its quantile function and order statistics are also included. Parameters of the distribution are estimated by the method of Maximum Likelihood estimation method along with Fisher information matrix and confidence intervals have also been given. The application has been discussed with the 30 years temperature data of Silchar city, Assam, India. The goodness of fit of the proposed distribution has been compared with Frechet distribution and as a result, for all 12 months, the proposed distribution fits better than the Frechet distribution.

Transmuted Erlang-Truncated Exponential Distribution

2016 ◽  
Vol 31 (2) ◽  
Author(s):  
Idika E. Okorie ◽  
Anthony C. Akpanta ◽  
Johnson Ohakwe
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Hazard Rate ◽  
Likelihood Estimation ◽  
Rate Function ◽  
Lifetime Distribution ◽  
Hazard Rate Function ◽  
Method Of Maximum Likelihood ◽  
Two Parameter ◽  
New Distribution

AbstractThis article introduces a new lifetime distribution called the transmuted Erlang-truncated exponential (TETE) distribution. This new distribution generalizes the two parameter Erlang-truncated exponential (ETE) distribution. Closed form expressions for some of its distributional and reliability properties are provided. The method of maximum likelihood estimation was proposed for estimating the parameters of the TETE distribution. The hazard rate function of the TETE distribution can be constant, increasing or decreasing depending on the value of the transmutation parameter

Exponentiated–Exponential Logistic Distribution: Some Properties and Application

2020 ◽  
Vol 9 (1) ◽  
pp. 100-108
Author(s):  
Laxmi Prasad Sapkota
Keyword(s):  
Hazard Rate ◽  
Likelihood Estimation ◽  
Quantile Function ◽  
Rate Function ◽  
Logistic Distribution ◽  
Hazard Rate Function ◽  
Density Plot ◽  
Mathematical Properties ◽  
And Behavior ◽  
New Distribution

This study proposes new distribution which is generated from exponentiated-exponential-X family of distribution. It is explored various shape and behavior of the observed distribution through probability density plot, hazard rate function and quantile function. Further we have investigated some mathematical properties, estimation of the parameters and associated confidence interval using maximum likelihood estimation (MLE) method of the exponentiatedexponential-logistic distribution (EELD).

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