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 Half-Logistic Lomax Distribution for Lifetime Modeling

2018 ◽  
Vol 2018 ◽  
pp. 1-12 ◽  
Author(s):  
Masood Anwar ◽  
Jawaria Zahoor
Keyword(s):  
Maximum Likelihood ◽  
Residual Life ◽  
Information Matrix ◽  
Simulated Data ◽  
Quantile Function ◽  
Rate Function ◽  
Mean Residual Life ◽  
Data Sets ◽  
Estimation Of Parameters ◽  
Proposed Model

We introduce a new two-parameter lifetime distribution called the half-logistic Lomax (HLL) distribution. The proposed distribution is obtained by compounding half-logistic and Lomax distributions. We derive some mathematical properties of the proposed distribution such as the survival and hazard rate function, quantile function, mode, median, moments and moment generating functions, mean deviations from mean and median, mean residual life function, order statistics, and entropies. The estimation of parameters is performed by maximum likelihood and the formulas for the elements of the Fisher information matrix are provided. A simulation study is run to assess the performance of maximum-likelihood estimators (MLEs). The flexibility and potentiality of the proposed model are illustrated by means of real and simulated data sets.

scholarly journals On The Transmuted Powered Moment Exponential Distribution

2021 ◽  
pp. 32-46
Author(s):  
Zafar Iqbal ◽  
Muhammad Rashad ◽  
Abdur Razaq ◽  
Muhammad Salman ◽  
Afsheen Javed
Keyword(s):  
Maximum Likelihood ◽  
Exponential Distribution ◽  
Survival Function ◽  
Likelihood Estimation ◽  
Real Data ◽  
Quantile Function ◽  
Rate Function ◽  
Data Sets ◽  
Inequality Measures ◽  
New Class

We introduce a new class of lifetime models called the transmuted powered moment exponential distribution. More specifically, the transmuted powered moment exponential distribution covers several new distributions. Survival analysis including survival function, hazard rate function and other related measures are computed. Analytical expressions for various mathematical properties of TPMED including rth moment, quantile function, inequality measures, and parameters are estimated by using maximum likelihood estimation and order statistics are also derived. A simulation study of the proposed distribution is performed. It is discovered that the Maximum Likelihood Estimators are consistent since the bias and Mean Square Error approach to zero when the sample size increases. The usefulness of the model associated with this distribution is illustrated by two real data sets and the new model provides a better fit than the models provided in literature.

scholarly journals Exponentiated Cubic Transmuted Weibull Distribution: Properties and Application

2021 ◽  
pp. 1-11
Author(s):  
Oseghale O. I. ◽  
Akomolafe A. A. ◽  
Gayawan E.
Keyword(s):  
Weibull Distribution ◽  
Real Life ◽  
Likelihood Estimation ◽  
Real Data ◽  
Quantile Function ◽  
Moment Generating Function ◽  
Data Sets ◽  
Estimation Technique ◽  
Life Data ◽  
Real Life Data

This work is focused on the four parameters Exponentiated Cubic Transmuted Weibull distribution which mostly found its application in reliability analysis most especially for data that are non-monotone and Bi-modal. Structural properties such as moment, moment generating function, Quantile function, Renyi entropy, and order statistics were investigated. The maximum likelihood estimation technique was used to estimate the parameters of the distribution. Application to two real-life data sets shows the applicability of the distribution in modeling real data.

Jaya algorithm in estimation of P[X > Y] for two parameter Weibull distribution

2022 ◽  
Vol 7 (2) ◽  
pp. 2820-2839
Author(s):  
Saurabh L. Raikar ◽  
◽  
Dr. Rajesh S. Prabhu Gaonkar ◽  
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Weibull Distribution ◽  
Least Squares ◽  
Weighted Least Squares ◽  
Real Life ◽  
Likelihood Estimation ◽  
Estimation Methods ◽  
Jaya Algorithm ◽  
Two Parameter

<abstract> <p>Jaya algorithm is a highly effective recent metaheuristic technique. This article presents a simple, precise, and faster method to estimate stress strength reliability for a two-parameter, Weibull distribution with common scale parameters but different shape parameters. The three most widely used estimation methods, namely the maximum likelihood estimation, least squares, and weighted least squares have been used, and their comparative analysis in estimating reliability has been presented. The simulation studies are carried out with different parameters and sample sizes to validate the proposed methodology. The technique is also applied to real-life data to demonstrate its implementation. The results show that the proposed methodology's reliability estimates are close to the actual values and proceeds closer as the sample size increases for all estimation methods. Jaya algorithm with maximum likelihood estimation outperforms the other methods regarding the bias and mean squared error.</p> </abstract>

scholarly journals A New Generalization of the Generalized Inverse Rayleigh Distribution with Applications

Symmetry ◽  
2021 ◽  
Vol 13 (4) ◽  
pp. 711
Author(s):  
Rana Ali Bakoban ◽  
Ashwaq Mohammad Al-Shehri
Keyword(s):  
Generalized Inverse ◽  
Real Life ◽  
Likelihood Estimation ◽  
Real Data ◽  
Quantile Function ◽  
Reliability Function ◽  
Rayleigh Distribution ◽  
Information Criteria ◽  
Difference Fields ◽  
The Mean

In this article, a new four-parameter lifetime model called the beta generalized inverse Rayleigh distribution (BGIRD) is defined and studied. Mixture representation of this model is derived. Curve’s behavior of probability density function, reliability function, and hazard function are studied. Next, we derived the quantile function, median, mode, moments, harmonic mean, skewness, and kurtosis. In addition, the order statistics and the mean deviations about the mean and median are found. Other important properties including entropy (Rényi and Shannon), which is a measure of the uncertainty for this distribution, are also investigated. Maximum likelihood estimation is adopted to the model. A simulation study is conducted to estimate the parameters. Four real-life data sets from difference fields were applied on this model. In addition, a comparison between the new model and some competitive models is done via information criteria. Our model shows the best fitting for the real data.

scholarly journals A Generalized Modification of the Kumaraswamy Distribution for Modeling and Analyzing Real-Life Data

2020 ◽  
Vol 8 (2) ◽  
pp. 521-548
Author(s):  
Rafid Alshkaki
Keyword(s):  
Real Life ◽  
Estimation Method ◽  
Simulated Data ◽  
Likelihood Estimation ◽  
Data Sets ◽  
Kumaraswamy Distribution ◽  
Life Data ◽  
Real Life Data ◽  
Beta Power ◽  
Special Cases

In this paper, a generalized modification of the Kumaraswamy distribution is proposed, and its distributional and characterizing properties are studied. This distribution is closed under scaling and exponentiation, and has some well-known distributions as special cases, such as the generalized uniform, triangular, beta, power function, Minimax, and some other Kumaraswamy related distributions. Moment generating function, Lorenz and Bonferroni curves, with its moments consisting of the mean, variance, moments about the origin, harmonic, incomplete, probability weighted, L, and trimmed L moments, are derived. The maximum likelihood estimation method is used for estimating its parameters and applied to six different simulated data sets of this distribution, in order to check the performance of the estimation method through the estimated parameters mean squares errors computed from the different simulated sample sizes. Finally, four real-life data sets are used to illustrate the usefulness and the flexibility of this distribution in application to real-life data.  

scholarly journals On modified Kies distribution and its applications

2017 ◽  
Vol 51 (1) ◽  
pp. 41-60
Author(s):  
C. SATHEESH KUMAR ◽  
S. H. S. DHARMAJA
Keyword(s):  
Maximum Likelihood ◽  
Hazard Function ◽  
Real Life ◽  
Simulated Data ◽  
Maximum Likelihood Estimators ◽  
Data Sets ◽  
Life Data ◽  
Real Life Data ◽  
Method Of Maximum Likelihood ◽  
Simulated Data Sets

In this paper, we consider a class of bathtub-shaped hazard function distribution through modifying the Kies distribution and investigate some of its important properties by deriving expressions for its percentile function, raw moments, stress-strength reliability measure etc. The parameters of the distribution are estimated by the method of maximum likelihood and discussed some of its reliability applications with the help of certain real life data sets. In addition, the asymptotic behavior of the maximum likelihood estimators of the parameters of the distribution is examined by using simulated data sets.

scholarly journals Properties, Inference and Applications of Alpha Power Extended Inverted Weibull Distribution

2020 ◽  
Vol 9 (6) ◽  
pp. 90
Author(s):  
A. A. Ogunde ◽  
S. T. Fayose ◽  
B. Ajayi ◽  
D. O. Omosigho
Keyword(s):  
Weibull Distribution ◽  
Information Matrix ◽  
Real Life ◽  
Simulation Method ◽  
Quantile Function ◽  
Transformation Method ◽  
Model Parameters ◽  
Data Sets ◽  
Alpha Power ◽  
Real Life Data

In this work, we introduce a new generalization of the Inverted Weibull distribution called the alpha power Extended Inverted Weibull distribution using the alpha power transformation method. This approach adds an extra parameter to the baseline distribution. The statistical properties of this distribution including the mean, variance, coefficient of variation, quantile function, median, ordinary and incomplete moments, skewness, kurtosis, moment and moment generating functions, reliability analysis, Lorenz and Bonferroni and curves, R&eacute;nyi of entropy and order statistics are studied. We consider the method of maximum likelihood for estimating the model parameters and the observed information matrix is derived. Simulation method and three real life data sets are presented to demonstrate the effectiveness of the new model.

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.

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