scholarly journals Statistical Modelling with Birnbaum-Saunders Distribution

2021 ◽  
pp. 30-36
Author(s):  
Nuri Celik
Keyword(s):  
Maximum Likelihood ◽  
Reliability Analysis ◽  
Real Life ◽  
Statistical Modelling ◽  
Likelihood Method ◽  
Type I ◽  
Type I Errors ◽  
Monte Carlo Simulation Study ◽  
Nonnormal Distribution ◽  
Error Terms

In this article, it is assumed that the distribution of the error terms is the Birnbaum-Saunders distribution in the process of one-way ANOVA. The Birnbaum-Saunders distribution has been widely used in reliability analysis especially in fatigue-life models. In reliability analysis, nonnormal distribution is much more common than the normal distribution. We obtain the estimation of the parameters og interest by maximum likelihood method. We also propose new test statistics based on these estimators . The efficiencies of the maximum likelihood estimators and the Type I errors obtained by using the proposed estimators are compared with normal theory via Monte Carlo simulation study. At the end of the study, the real life example is given just for the illustration of the method.

scholarly journals Robustness Test of Selected Estimators of Linear Regression with Autocorrelated Error Term: A Monte-Carlo Simulation Study

2021 ◽  
pp. 1-17
Author(s):  
Rauf Ibrahim Rauf ◽  
Okoli Juliana Ifeyinwa ◽  
Haruna Umar Yahaya
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Maximum Likelihood ◽  
Linear Regression ◽  
Simulation Study ◽  
Explanatory Variable ◽  
Real Life ◽  
Least Square ◽  
Monte Carlo Simulation Study ◽  
Error Terms

Assumptions in the classical linear regression model include that of lack of autocorrelation of the error terms and the zero covariance between the explanatory variable and the error terms. This study is channeled towards the estimation of the parameters of the linear models for both time series and cross-sectional data when the above two assumptions are violated. The study used the Monte-Carlo simulation method to investigate the performance of six estimators: ordinary least square (OLS), Prais-Winsten (PW), Cochrane-Orcutt (CC), Maximum Likelihood (MLE), Restricted Maximum- Likelihood (RMLE) and the Weighted Least Square (WLS) in estimating the parameters of a single linear model in which the explanatory variable is also correlated with the autoregressive error terms. Using the models’ finite properties(mean square error) to measure the estimators’ performance, the results shows that OLS should be preferred when autocorrelation level is relatively mild (ρ = 0.3) and the PW, CC, RMLE, and MLE estimator will perform better with the presence of any level of AR (1) disturbance between 0.4 to 0.8 level, while WLS shows better performance at 0.9 level of autocorrelation and above. The study thus recommended the application of the various estimators considered to real-life data to affirm the results of this simulation study.

scholarly journals A Study on A New Type 1 Half-Logistic Family of Distributions and Its Applications

2020 ◽  
Vol 8 (4) ◽  
pp. 934-949
Author(s):  
Morad Alizadeh ◽  
Alireza Nematollahi ◽  
Emrah Altun ◽  
Mahdi Rasekhi
Keyword(s):  
Residual Life ◽  
Moment Generating Function ◽  
Likelihood Method ◽  
Mean Deviation ◽  
Model Parameters ◽  
Type I ◽  
Monte Carlo Simulation Study ◽  
New Type ◽  
Application Fields ◽  
Family Of Distributions

In this paper, we propose a new class of continuous distributions with two extra shape parameters called the a new type I half logistic-G family of distributions. Some of important properties including ordinary moments, quantiles, moment generating function, mean deviation, moment of residual life, moment of reversed residual life, order statistics and extreme value are obtained. To estimate the model parameters, the maximum likelihood method is also applied by means of Monte Carlo simulation study. A new location-scale regression model based on the new type I half logistic-Weibull distribution is then introduced. Applications of the proposed family is demonstrated in many fields such as survival analysis and univariate data fitting. Empirical results show that the proposed models provide better fits than other well-known classes of distributions in many application fields.

The Poisson Nadarajah–Haghighi Distribution: Properties and Applications to Lifetime Data

2019 ◽  
Vol 27 (01) ◽  
pp. 2050005
Author(s):  
Muhammad Mansoor ◽  
M. H. Tahir ◽  
Aymaan Alzaatreh ◽  
Gauss M. Cordeiro
Keyword(s):  
Maximum Likelihood ◽  
Censored Data ◽  
Survival Data ◽  
Maximum Likelihood Method ◽  
Likelihood Estimation ◽  
Real Data ◽  
Likelihood Method ◽  
Lifetime Data ◽  
Monte Carlo Simulation Study ◽  
Mathematical Properties

A new three-parameter compounded extended-exponential distribution “Poisson Nadarajah–Haghighi” is introduced and studied, which is quite flexible and can be used effectively in modeling survival data. It can have increasing, decreasing, upside-down bathtub and bathtub-shaped failure rate. A comprehensive account of the mathematical properties of the model is presented. We discuss maximum likelihood estimation for complete and censored data. The suitability of the maximum likelihood method to estimate its parameters is assessed by a Monte Carlo simulation study. Four empirical illustrations of the new model are presented to real data and the results are quite satisfactory.

scholarly journals Statistical Tests for the Reciprocal of a Normal Mean with a Known Coefficient of Variation

2015 ◽  
Vol 2015 ◽  
pp. 1-5
Author(s):  
Wararit Panichkitkosolkul
Keyword(s):  
Monte Carlo Simulation ◽  
Coefficient Of Variation ◽  
Statistical Tests ◽  
Taylor Series Expansion ◽  
Type I ◽  
Type I Errors ◽  
Monte Carlo Simulation Study ◽  
Asymptotic Test ◽  
Normal Mean ◽  
Simulation Results

An asymptotic test and an approximate test for the reciprocal of a normal mean with a known coefficient of variation were proposed in this paper. The asymptotic test was based on the expectation and variance of the estimator of the reciprocal of a normal mean. The approximate test used the approximate expectation and variance of the estimator by Taylor series expansion. A Monte Carlo simulation study was conducted to compare the performance of the two statistical tests. Simulation results showed that the two proposed tests performed well in terms of empirical type I errors and power. Nevertheless, the approximate test was easier to compute than the asymptotic test.

Comparing the Variances of Two Dependent Groups

1990 ◽  
Vol 15 (3) ◽  
pp. 237-247 ◽  
Author(s):  
Rand R. Wilcox
Keyword(s):  
Maximum Likelihood ◽  
Low Power ◽  
Maximum Likelihood Estimate ◽  
Type I ◽  
Type Ii ◽  
Type I Errors ◽  
Satisfactory Solution ◽  
Scheffe Test ◽  
Modified Maximum Likelihood ◽  
Type Ii Errors

Let X and Y be dependent random variables with variances σ2x and σ2y. Recently, McCulloch (1987) suggested a modification of the Morgan-Pitman test of Ho: σ2x=σ2y But, as this paper describes, there are situations where McCulloch’s procedure is not robust. A subsample approach, similar to the Box-Scheffe test, is also considered and found to give conservative results, in terms of Type I errors, for all situations considered, but it yields relatively low power. New results on the Sandvik-Olsson procedure are also described, but the procedure is found to be nonrobust in situations not previously considered, and its power can be low relative to the two other techniques considered here. A modification of the Morgan-Pitman test based on the modified maximum likelihood estimate of a correlation is also considered. This last procedure appears to be robust in situations where the Sandvik-Olsson (1982) and McCulloch procedures are robust, and it can have more power than the Sandvik-Olsson. But it too gives unsatisfactory results in certain situations. Thus, in terms of power, McCulloch’s procedure is found to be best, with the advantage of being simple to use. But, it is concluded that, in terms of controlling both Type I and Type II errors, a satisfactory solution does not yet exist.

scholarly journals The Zubair-Inverse Lomax Distribution with Applications

2020 ◽  
pp. 1-14
Author(s):  
Jamilu Yunusa Falgore
Keyword(s):  
Maximum Likelihood ◽  
Moment Generating Function ◽  
Likelihood Method ◽  
Model Parameters ◽  
Data Sets ◽  
Monte Carlo Simulation Study ◽  
New Model ◽  
Inverse Lomax Distribution ◽  
The Right ◽  
Decreasing Functions

In this article, an extension of Inverse Lomax (IL) distribution with the Zubair-G family is considered . Various statistical properties of the new model where derived, including moment generating function, R´enyi entropy, and order statistics. A Monte Carlo simulation study was presented to evaluate the performance of the maximum likelihood estimators. The new model can be skew to the right, constant, and decreasing functions depending on the parameter values.We discussed the estimation of the model parameters by maximum likelihood method. The application of the new model to the data sets indicates that the new model is better than the existing competitors as it has minimum value of statistics criteria.

scholarly journals A New Family of Continuous Probability Distributions

Entropy ◽  
2021 ◽  
Vol 23 (2) ◽  
pp. 194
Author(s):  
M. El-Morshedy ◽  
Fahad Sameer Alshammari ◽  
Yasser S. Hamed ◽  
Mohammed S. Eliwa ◽  
Haitham M. Yousof
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Method ◽  
Probability Distributions ◽  
Real Life ◽  
Likelihood Method ◽  
Model Parameters ◽  
Finite Sample ◽  
Graphical Simulation ◽  
New Family ◽  
The One

In this paper, a new parametric compound G family of continuous probability distributions called the Poisson generalized exponential G (PGEG) family is derived and studied. Relevant mathematical properties are derived. Some new bivariate G families using the theorems of “Farlie-Gumbel-Morgenstern copula”, “the modified Farlie-Gumbel-Morgenstern copula”, “the Clayton copula”, and “the Renyi’s entropy copula” are presented. Many special members are derived, and a special attention is devoted to the exponential and the one parameter Pareto type II model. The maximum likelihood method is used to estimate the model parameters. A graphical simulation is performed to assess the finite sample behavior of the estimators of the maximum likelihood method. Two real-life data applications are proposed to illustrate the importance of the new family.

Comparison of Methods Used to Estimate Age and Length of Fishes at Sexual Maturity Using Populations of White Sucker (Catostomus commersoni)

1991 ◽  
Vol 48 (8) ◽  
pp. 1446-1459 ◽  
Author(s):  
Edward A. Trippel ◽  
Harold H. Harvey
Keyword(s):  
Maximum Likelihood ◽  
Sexual Maturity ◽  
Probit Analysis ◽  
Likelihood Method ◽  
Type I ◽  
White Sucker ◽  
Age At Maturity ◽  
Catostomus Commersoni ◽  
Type Iv ◽  
First Occurrence

We compared six methods of estimating age and length at sexual maturity of iteroparous fishes: probit analysis, maximum likelihood methodology, linear regression on arcsine - square root transformed data, Lysack's formula, visual observation of distributions for the first occurrence of [Formula: see text] maturity, and computation of lt of the von Bertalanffy equation using age at maturity for t. To aid comparisons, we subdivided 32 white sucker (Catostomus commersoni) maturity distributions into four types: abrupt transition to maturity (type I), successive increases in proportion mature with increase in age or length (type II), nonsuccessive increases in proportion mature with increase in age or length (type III), and absence of 100% maturity at any age (type IV). Type I distributions were best represented by reporting the first occurrence of [Formula: see text] maturity, types II and III by probit analysis and the maximum likelihood method, and type IV distributions were not adequately represented by any method. Lysack's formula tended to produce high estimates for types II and III and negative values for some type IV distributions. Both the number and position of missing year classes influenced estimates of age at maturity. We recommend documenting maturity distributions with all estimates of age and size at maturity.

scholarly journals A New Kumaraswamy Generalized Family of Distributions with Properties, Applications and Bivariate Extension

2020 ◽  
Author(s):  
Muhammad H. Tahir ◽  
Muhammad Adnan Hussain ◽  
Gauss Cordeiro ◽  
Mahmoud El-Morshedy ◽  
Mohammed S. Eliwa
Keyword(s):  
Maximum Likelihood ◽  
Real Life ◽  
Unit Interval ◽  
Likelihood Method ◽  
Data Sets ◽  
Data Set ◽  
Life Data ◽  
Real Life Data ◽  
The Family ◽  
Family Of Distributions

For bounded unit interval, we propose a new Kumaraswamy generalized (G) family of distributions from a new generator which could be an alternate to the Kumaraswamy-G family proposed earlier by Cordeiro and de-Castro in 2011. This new generator can also be used to develop alternate G-classes such as beta-G, McDonald-G, Topp-Leone-G, Marshall-Olkin-G and Transmuted-G for bounded unit interval. Some mathematical properties of this new family are obtained and maximum likelihood method is used for estimating the family parameters. We investigate the properties of one special model called a new Kumaraswamy-Weibull (NKwW) distribution. Parameter estimation is dealt and maximum likelihood estimators are assessed through simulation study. Two real life data sets are analyzed to illustrate the importance and flexibility of this distribution. In fact, this model outperforms some generalized Weibull models such as the Kumaraswamy-Weibull, McDonald-Weibull, beta-Weibull, exponentiated-generalized Weibull, gamma-Weibull, odd log-logistic-Weibull, Marshall-Olkin-Weibull, transmuted-Weibull, exponentiated-Weibull and Weibull distributions when applied to these data sets. The bivariate extension of the family is proposed and the estimation of parameters is given. The usefulness of the bivariate NKwW model is illustrated empirically by means of a real-life data set.

scholarly journals Estimation for inverse Gaussian distribution under first-failure progressive hybird censored samples

Filomat ◽  
2017 ◽  
Vol 31 (18) ◽  
pp. 5743-5752 ◽  
Author(s):  
Jun-Mei Jia ◽  
Zai-Zai Yan ◽  
Xiu-Yun Peng
Keyword(s):  
Gaussian Distribution ◽  
Information Matrix ◽  
Real Life ◽  
Inverse Gaussian Distribution ◽  
Type I ◽  
Inverse Gaussian ◽  
Bayes Estimators ◽  
Monte Carlo Simulation Study ◽  
Highest Posterior Density ◽  
Censoring Scheme

In this paper, a first-failure progressive hybird censoring scheme is introduced that combines progressive first-failure censoring and Type-I censoring. We obtain the maximum likelihood estimators (MLEs) and the Bayes estimators of the unknown parameters from the inverse Gaussian distribution based on the first-failure progressive hybird censoring scheme. The Bayes estimates are computed under squared error, Linex and general entropy loss functions. The asymptotic confidence intervals and coverage probabilities for the parameters are obtained based on the observed Fisher?s information matrix. Also, highest posterior density credible intervals for the parameters are computed using Gibbs sampling procedure. A Monte Carlo simulation study is conducted in order to compare the Bayes estimators with the MLEs. Real life data sets are provided to illustration purposes.

Sign in / Sign up

Export Citation Format

Share Document