scholarly journals Parametric Interval Estimation of the Geeta Distribution

2018 ◽  
Vol 8 (1) ◽  
pp. 1
Author(s):  
Betty C. Korir ◽  
Josphat K. Kinyanjui
Keyword(s):  
Confidence Interval ◽  
Interval Estimation ◽  
Random Variable ◽  
Moment Generating Function ◽  
Distribution Model ◽  
Unknown Parameters ◽  
Sample Mean ◽  
Population Mean ◽  
Point Estimator ◽  
Interval Estimators

It is well known that the sample mean is the estimator of a population mean in mathematical statistics from a given population of interest as a point estimator which assume a single number that is obtained by taking a random sample of a specified size from the entire population, depending on whether the population mean and variance is known or unknown. In the interval estimation, the sample mean is accompanied with a plus or a minus margin of an error that is assumed that the estimator is contained within the range of values with certain degree of confidence. This paper investigated and obtained the interval estimators of the unknown constants of Geeta distribution model through the construction of confidence interval using; the pivotal quantity method, the shortest-length confidence interval, unbiased confidence interval estimators, Bayesian confidence interval estimators and statistical method. Geeta distribution is a new discrete random variable distribution defined over all the positive integers, with two unknown parameters. The properties and characteristics of the Geeta distribution model were discussed and reviewed that is, the existence of the mean, variance, moment generating function and that the sum of all probabilities is unity. These are common properties of any given probability density function.

scholarly journals Survival estimation for singly type one censored sample based on generalized Rayleigh distribution

2014 ◽  
Vol 11 (2) ◽  
pp. 193-201
Author(s):  
Baghdad Science Journal
Keyword(s):  
Current Model ◽  
Survival Function ◽  
Information Matrix ◽  
Interval Estimation ◽  
Real Data ◽  
Rayleigh Distribution ◽  
Point Estimation ◽  
Distribution Model ◽  
Unknown Parameters ◽  
Generalized Rayleigh Distribution

This paper interest to estimation the unknown parameters for generalized Rayleigh distribution model based on censored samples of singly type one . In this paper the probability density function for generalized Rayleigh is defined with its properties . The maximum likelihood estimator method is used to derive the point estimation for all unknown parameters based on iterative method , as Newton – Raphson method , then derive confidence interval estimation which based on Fisher information matrix . Finally , testing whether the current model ( GRD ) fits to a set of real data , then compute the survival function and hazard function for this real data.

The Back Page: My Favorite Lesson: Perfect Sample and Population Mean Formula

2013 ◽  
Vol 107 (4) ◽  
pp. 320
Author(s):  
Clarence W. Lienhard
Keyword(s):  
Random Variable ◽  
Mass Function ◽  
Probability Mass Function ◽  
Discrete Random Variable ◽  
Sample Mean ◽  
Population Mean ◽  
Probability Mass

Typically, students readily understand the concepts of the sample mean and a discrete random variable X with its probability mass function. However, they find the population mean formula unduly difficult to comprehend. Using a perfect sample, the author guides readers to discover the population mean formula from the sample mean.

scholarly journals A New Poisson Inverted Exponential Distribution: Model, Properties and Application

2020 ◽  
pp. 136-146
Author(s):  
Govinda Prasad Dhungana
Keyword(s):  
Exponential Distribution ◽  
Goodness Of Fit ◽  
Residual Life ◽  
Life Time ◽  
Real Data ◽  
Quantile Function ◽  
Moment Generating Function ◽  
Distribution Model ◽  
Time Data ◽  
Unknown Parameters

A new Poisson Inverted Exponential distribution is developed from the Poisson family of distribution, which has two parameters. The characteristic of the intended model is unimodal, positive skewed and platykurtic, while the characteristic of the hazard function is the inverted bathtub and the decreasing order. Explicit expression of quantile function, moments (including incomplete and conditional moments), moment generating function, residual life function, R`enyi and q-entropies, probability weighted moment and order statistics of the intended model. The value of unknown parameters is estimated by the maximum likelihood estimate with the confidence interval. Similarly, purposed model compared with well-known other five distributions through different criteria like as goodness of fit, P-P plot, Q-Q plots and K-S test. Likewise, we fitted the PDF and CDF of purposed model with other models, it is clear that intended model is great flexibility and satisfactory fit than those models. Therefore purposed model is more useful in real data and life time data analysis and modelling.

scholarly journals Understanding the Difference Between Standard Deviation and Standard Error of the Mean, and Knowing When to Use Which

2020 ◽  
Vol 42 (4) ◽  
pp. 409-410
Author(s):  
Chittaranjan Andrade
Keyword(s):  
Standard Deviation ◽  
Confidence Interval ◽  
Standard Error ◽  
Statistical Significance ◽  
Sample Mean ◽  
Population Mean ◽  
Sample Data ◽  
The Mean ◽  
The Difference

Many authors are unsure of whether to present the mean along with the standard deviation (SD) or along with the standard error of the mean (SEM). The SD is a descriptive statistic that estimates the scatter of values around the sample mean; hence, the SD describes the sample. In contrast, the SEM is an estimate of how close the sample mean is to the population mean; it is an intermediate term in the calculation of the 95% confidence interval around the mean, and (where applicable) statistical significance; the SEM does not describe the sample. Therefore, the mean should always be accompanied by the SD when describing the sample. There are many reasons why the SEM continues to be reported, and it is argued that none of these is justifiable. In fact, presentation of SEMs may mislead readers into believing that the sample data are more precise than they actually are. Given that the standard error is not presented for other parameters, such as difference between means or proportions, and difference between proportions, it is suggested that presentation of SEM values can be done away with, altogether.

scholarly journals Interval Estimation of Stress-Strength Reliability for a General Exponential Form Distribution with Different Unknown Parameters

2017 ◽  
Vol 6 (6) ◽  
pp. 60 ◽  
Author(s):  
Nahed A. Mokhlis ◽  
Emad J. Ibrahim ◽  
Dina M. Gharieb
Keyword(s):  
Weibull Distribution ◽  
Simulation Study ◽  
Average Length ◽  
Interval Estimation ◽  
Numerical Comparison ◽  
Unknown Parameters ◽  
Exponential Form ◽  
Distribution Parameters ◽  
Interval Estimators

This paper deals with interval estimation of the stress-strength reliability, when the stress and strength variables follow a general exponential form distribution. The distribution parameters of both the stress and the strength are assumed to be unknown. Interval estimation for reliability is discussed, using different approaches. The results obtained are applicable to many well known distributions. For illustration of the general results obtained a simulation study is performed with application on Weibull distribution. Numerical comparison of the interval estimators is carried out based on average length, probability coverage, and tail errors.

scholarly journals INTERVAL ESTIMATION OF DISTRIBUTION PARAMETER BY STATISTICAL TRIALS OF EXPECTED VALUE

2019 ◽  
pp. 138-143
Author(s):  
V.O. Barannik
Keyword(s):  
Numerical Approximation ◽  
Interval Estimation ◽  
Random Variable ◽  
Expected Value ◽  
Distribution Parameter ◽  
Upper And Lower Bounds ◽  
Distribution Parameters ◽  
Estimation Of Distribution ◽  
Parameter Interval ◽  
Interval Estimators

The distribution parameter interval estimators are obtained by direct numerical approximation of the expected value for infinite and finite populations under the known upper and lower bounds of the random variable domain. Like in Bayesian approach, the distribution parameters are treated as random variables, and their uncertainty is described as a distribution. The Monte Carlo procedure is involved to get the correspondent confidence interval endpoints. The model does not impose any restrictions on the type of distributions. In contrast to other nonparametric interval assessments of distribution parameters, the model is operable for samples of any size.

The Numerical and its Application in the Interval Estimates and Hypothesis Test

2010 ◽  
Vol 143-144 ◽  
pp. 1391-1395
Author(s):  
Xin Chun Wang ◽  
Xing Hua Ma ◽  
Bing Han
Keyword(s):  
Confidence Interval ◽  
Hypothesis Testing ◽  
Statistical Inference ◽  
Hypothesis Test ◽  
Interval Estimation ◽  
Parameters Estimation ◽  
Unknown Parameters ◽  
Significance Level ◽  
The Relationship ◽  
Statistical Work

The whole unknown parameters estimation and hypothesis testing is the most common and most commonly used statistical inference,so clarify the relationship between them is very important.Clearing both unity and not uniformity will help to amend the emergence of some specious argument of statistical work. In this paper, some differences were analyzed on interval estimation and hypothesis testing of statistical inference theory,the scope of their application of two methods was discussed, the dualityof Neyman —Pearson hypothesis testing and confidence interval was described Then provided the method of determining the unknown parameters’ confidence interval in hypothesis test.at the same time, it provided the ideas how to solve the problem of refusal field of hypothesis test througn confidence interval . As the confidence interval of the statistics varies with the selected significance level and sample size, it is heavily influenced by subjective factors.

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