scholarly journals Transmuted Alpha Power Inverse Rayleigh Distribution: Properties and Application

2019 ◽  
Vol 11 (2) ◽  
pp. 185-194
Author(s):  
A. S. Malik ◽  
S. P. Ahmad
Keyword(s):  
Parameter Estimation ◽  
Potential Application ◽  
Real Life ◽  
Rayleigh Distribution ◽  
Parameter Distribution ◽  
Alpha Power ◽  
Data Set ◽  
Life Data ◽  
Real Life Data ◽  
Proposed Model

This paper proposes a new three parameter-distribution through the technique known as Transmutation. The proposed distribution is named Transmuted Alpha power inverse Rayleigh Distribution. Several important properties of the distribution are derived. The parameter estimation is also carried out. Two real life data set are used at the end to describe the potential application of proposed model.

scholarly journals A Study of Some Properties and Goodness-of-Fit of a Gompertz-Rayleigh Model

2020 ◽  
pp. 18-31
Author(s):  
Fadimatu Bawuro Mohammed ◽  
Kabiru Ahmed Manju ◽  
Umar Kabir Abdullahi ◽  
Makama Musa Sani ◽  
Samson Kuje
Keyword(s):  
Goodness Of Fit ◽  
Real Life ◽  
Likelihood Estimation ◽  
Rayleigh Distribution ◽  
Parameter Distribution ◽  
Applied Statistics ◽  
Life Data ◽  
Real Life Data ◽  
Method Of Maximum Likelihood ◽  
Wide Range

The Rayleigh was obtained from the amplitude of sound resulting from many important sources by Rayleigh. It is continuous probability distribution with a wide range of applications such as in life testing experiments, reliability analysis, applied statistics and clinical studies. However, it is not flexible enough for modeling heavily skewed datasets as compared to compound distributions. In this paper, we introduce a new extension of the Rayleigh distribution by using a Gompertz-G family of distributions. This paper defines and studies a three-parameter distribution called “Gompertz-Rayleigh distribution”. Some properties of the proposed distribution are derived and discussed comprehensively in this paper and the three parameters are estimated using the method of maximum likelihood estimation. The goodness-of-fit of the proposed distribution is also evaluated by fitting it in comparison with some other existing distributions using a real life data.

scholarly journals Calibration-Based Estimators using Different Distance Measures under Two Auxiliary Variables: A Comparative Study

2021 ◽  
Vol 19 (1) ◽  
pp. 2-20
Author(s):  
Piyush Kant Rai ◽  
Alka Singh ◽  
Muhammad Qasim
Keyword(s):  
Mean Squared Error ◽  
Real Life ◽  
Distance Functions ◽  
Distance Measures ◽  
Auxiliary Variables ◽  
Data Set ◽  
Life Data ◽  
Squared Error ◽  
Real Life Data ◽  
Relative Root

This article introduces calibration estimators under different distance measures based on two auxiliary variables in stratified sampling. The theory of the calibration estimator is presented. The calibrated weights based on different distance functions are also derived. A simulation study has been carried out to judge the performance of the proposed estimators based on the minimum relative root mean squared error criterion. A real-life data set is also used to confirm the supremacy of the proposed method.

PROFIT ESTIMATION FOR A PRODUCT UNDER WARRANTY: AN EVALUATION BASED ON CUSTOMER'S EXPECTATION AND SATISFACTION

2014 ◽  
Vol 21 (06) ◽  
pp. 1450029 ◽  
Author(s):  
P. K. KAPUR ◽  
ADARSH ANAND ◽  
NITIN SACHDEVA
Keyword(s):  
Real Life ◽  
Fixed Cost ◽  
Inventory Cost ◽  
Data Set ◽  
Customer Complaints ◽  
Customer Expectation ◽  
Real Life Data ◽  
Proposed Model ◽  
The Difference ◽  
Warranty Claims

Performance of a product not as expected by the customer brings warranty expenditure into the picture. In other words, the deviation of the product performance (PP) from the customer expectation (CE) is the reason for customer complaints and warranty expenses. When this conflicting scenario occurs in market, warranty comes into existence and fulfilling warranty claims of customers adds to product's overall cost. In this paper, based on the difference between PP and CE about the product we estimate profit for the firm. Furthermore, factors like fixed cost, production cost and inventory cost have also been considered in framing the optimization problem. In the proposed model, a two-dimensional innovation diffusion model (TD-IDM) which combines the adoption time of technological diffusion and price of the product has been used. Classical Cobb–Douglas function that takes into account the technological adoptions and other dimensions explicitly has been used to structure the production function. The proposed model has been validated on real life data set.

scholarly journals A New Three-parameter Xgamma Fréchet Distribution with Different Methods of Estimation and Applications

2021 ◽  
pp. 291-308
Author(s):  
Mohamed Ibrahim Mohamed ◽  
Laba Handique ◽  
Subrata Chakraborty ◽  
Nadeem Shafique Butt ◽  
Haitham M. Yousof
Keyword(s):  
Real Life ◽  
Estimation Methods ◽  
Data Sets ◽  
Clear Preference ◽  
Life Data ◽  
Fréchet Distribution ◽  
Real Life Data ◽  
Proposed Model ◽  
Frechet Distribution

In this article an attempt is made to introduce a new extension of the Fréchet model called the Xgamma Fréchet model. Some of its properties are derived. The estimation of the parameters via different estimation methods are discussed. The performances of the proposed estimation methods are investigated through simulations as well as real life data sets. The potentiality of the proposed model is established through modelling of two real life data sets. The results have shown clear preference for the proposed model compared to several know competing ones.

scholarly journals Bayesian Analysis of Extended Cox Model with Time-Varying Covariates Using Bootstrap Prior

2020 ◽  
Vol 18 (2) ◽  
pp. 2-13
Author(s):  
Oyebayo Ridwan Olaniran ◽  
Mohd Asrul Affendi Abdullah
Keyword(s):  
Empirical Bayes ◽  
Cox Model ◽  
Real Life ◽  
Estimation Procedure ◽  
Time Varying ◽  
Data Set ◽  
Life Data ◽  
Real Life Data ◽  
Time Varying Covariates ◽  
Extended Cox Model

A new Bayesian estimation procedure for extended cox model with time varying covariate was presented. The prior was determined using bootstrapping technique within the framework of parametric empirical Bayes. The efficiency of the proposed method was observed using Monte Carlo simulation of extended Cox model with time varying covariates under varying scenarios. Validity of the proposed method was also ascertained using real life data set of Stanford heart transplant. Comparison of the proposed method with its competitor established appreciable supremacy of the method.

scholarly journals A New Generalized Transmuted Inverse Exponential Distribution: Properties and Application

2018 ◽  
pp. 1-13
Author(s):  
Uchenna U. Uwadi ◽  
Elebe E. Nwaezza
Keyword(s):  
Exponential Distribution ◽  
Real Life ◽  
Quantile Function ◽  
Moment Generating Function ◽  
Maximum Likelihood Estimates ◽  
Data Set ◽  
Real Life Data ◽  
Proposed Model ◽  
Inverse Exponential Distribution ◽  
The Moment

In this study, we proposed a new generalised transmuted inverse exponential distribution with three parameters and have transmuted inverse exponential and inverse exponential distributions as sub models. The hazard function of the distribution is nonmonotonic, unimodal and inverted bathtub shaped making it suitable for modelling lifetime data. We derived the moment, moment generating function, quantile function, maximum likelihood estimates of the parameters, Renyi entropy and order statistics of the distribution. A real life data set is used to illustrate the usefulness of the proposed model.     

scholarly journals An extensive extension of exponentiated exponential distribution using alpha power transformation – statistical properties and applications in engineering science

2021 ◽  
Vol 17 (2) ◽  
pp. 59-74
Author(s):  
S. Qurat Ul Ain ◽  
K. Ul Islam Rather
Keyword(s):  
Exponential Distribution ◽  
Real Life ◽  
Statistical Properties ◽  
Data Sets ◽  
Alpha Power ◽  
Real Life Data ◽  
Proposed Model ◽  
Mean Variance ◽  
New Distribution ◽  
Extra Parameter

Abstract In this article, an extension of exponentiated exponential distribution is familiarized by adding an extra parameter to the parent distribution using alpha power technique. The new distribution obtained is referred to as Alpha Power Exponentiated Exponential Distribution. Various statistical properties of the proposed distribution like mean, variance, central and non-central moments, reliability functions and entropies have been derived. Two real life data sets have been applied to check the flexibility of the proposed model. The new density model introduced provides the better fit when compared with other related statistical models.

scholarly journals An Extension of Log-Logistic Distribution for Analyzing Survival Data

2020 ◽  
pp. 789-801
Author(s):  
Aliya Syed Malik ◽  
S.P. Ahmad
Keyword(s):  
Survival Data ◽  
Real Life ◽  
Likelihood Estimation ◽  
Estimation Procedure ◽  
Logistic Distribution ◽  
Data Sets ◽  
Alpha Power ◽  
Real Life Data ◽  
Proposed Model ◽  
New Distribution

In this paper, a new generalization of Log Logistic Distribution using Alpha Power Transformation is proposed. The new distribution is named Alpha Power Log-Logistic Distribution. A comprehensive account of some of its statistical properties are derived. The maximum likelihood estimation procedure is used to estimate the parameters. The importance and utility of the proposed model are proved empirically using two real life data sets.

scholarly journals Graduation of term assurance data using frailty approach

2021 ◽  
Vol 16 (3) ◽  
pp. 2809-2823
Author(s):  
Walter Omonywa Onchere
Keyword(s):  
Real Life ◽  
Mortality Rates ◽  
Frailty Models ◽  
Data Set ◽  
Life Data ◽  
Real Life Data ◽  
Crude Mortality ◽  
Exponentiated Weibull ◽  
Weibull Models ◽  
Fully Bayesian

Frailty models have been used in literature to account for heterogeneity among insureds in-terms of mortality. In this article, we compare the gamma and the non-central gamma as frailty distributions with the exponentiated exponential and exponentiated Weibull as baseline hazards. We adopt a fully Bayesian approach to calibrate the baselines based on crude mortality rates from a major Kenyan insurer. Comparing the gamma-exponentiated Weibull with the non-central gamma-exponentiated Weibull models shows that the non-central gamma provides a good fit to the real life data-set and is therefore recommended for valuation.

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