Sample Size for a Specified Width Confidence Interval on the Variance of a Normal Distribution

Biometrics ◽  
1960 ◽  
Vol 16 (4) ◽  
pp. 636 ◽  
Author(s):  
Franklin A. Graybill ◽  
Robert D. Morrison
Keyword(s):  
Confidence Interval ◽  
Sample Size ◽  
Normal Distribution ◽  
Width Confidence Interval

scholarly journals Multistage Estimation of the Rayleigh Distribution Variance

Symmetry ◽  
2020 ◽  
Vol 12 (12) ◽  
pp. 2084
Author(s):  
Ali Yousef ◽  
Ayman A. Amin ◽  
Emad E. Hassan ◽  
Hosny I. Hamdy
Keyword(s):  
Confidence Interval ◽  
Sample Size ◽  
Interval Estimation ◽  
Sequential Estimation ◽  
Rayleigh Distribution ◽  
Point Estimation ◽  
Asymptotic Results ◽  
Squared Error Loss Function ◽  
Estimation Problems ◽  
Width Confidence Interval

In this paper we discuss the multistage sequential estimation of the variance of the Rayleigh distribution using the three-stage procedure that was presented by Hall (Ann. Stat. 9(6):1229–1238, 1981). Since the Rayleigh distribution variance is a linear function of the distribution scale parameter’s square, it suffices to estimate the Rayleigh distribution’s scale parameter’s square. We tackle two estimation problems: first, the minimum risk point estimation problem under a squared-error loss function plus linear sampling cost, and the second is a fixed-width confidence interval estimation, using a unified optimal stopping rule. Such an estimation cannot be performed using fixed-width classical procedures due to the non-existence of a fixed sample size that simultaneously achieves both estimation problems. We find all the asymptotic results that enhanced finding the three-stage regret as well as the three-stage fixed-width confidence interval for the desired parameter. The procedure attains asymptotic second-order efficiency and asymptotic consistency. A series of Monte Carlo simulations were conducted to study the procedure’s performance as the optimal sample size increases. We found that the simulation results agree with the asymptotic results.

scholarly journals COMPARACION DEL PROMEDIO Y LA MEDIANA COMO ESTIMADORES DE LA MEDIA PARA MUESTRAS NORMALES DEPENDIENDO DEL TAMAÑO DE MUESTRA

2017 ◽  
Vol 23 (2) ◽  
pp. 33
Author(s):  
José W. Camero Jiménez ◽  
Jahaziel G. Ponce Sánchez
Keyword(s):  
Confidence Interval ◽  
Sample Size ◽  
Normal Distribution ◽  
Confidence Intervals ◽  
Hypothesis Tests ◽  
Sample Mean ◽  
Palabras Clave ◽  
The Mean ◽  
The Difference

Actualmente los métodos para estimar la media son los basados en el intervalo de confianza del promedio o media muestral. Este trabajo pretende ayudar a escoger el estimador (promedio o mediana) a usar dependiendo del tamaño de muestra. Para esto se han generado, vía simulación en excel, muestras con distribución normal y sus intervalos de confianza para ambos estimadores, y mediante pruebas de hipótesis para la diferencia de proporciones se demostrará que método es mejor dependiendo del tamaño de muestra. Palabras clave.-Tamaño de muestra, Intervalo de confianza, Promedio, Mediana. ABSTRACTCurrently the methods for estimating the mean are those based on the confidence interval of the average or sample mean. This paper aims to help you choose the estimator (average or median) to use depending on the sample size. For this we have generated, via simulation in EXCEL, samples with normal distribution and confidence intervals for both estimators, and by hypothesis tests for the difference of proportions show that method is better depending on the sample size. Keywords.-Sampling size, Confidence interval, Average, Median.

Features of accumulation of amounts of measurement error

2017 ◽  
Vol 928 (10) ◽  
pp. 58-63 ◽  
Author(s):  
V.I. Salnikov
Keyword(s):  
Measurement Error ◽  
Confidence Interval ◽  
Normal Distribution ◽  
Confidence Level ◽  
Measurement Errors ◽  
Truncated Normal Distribution ◽  
Truncated Normal ◽  
The Law ◽  
Normal Law

The initial subject for study are consistent sums of the measurement errors. It is assumed that the latter are subject to the normal law, but with the limitation on the value of the marginal error Δpred = 2m. It is known that each amount ni corresponding to a confidence interval, which provides the value of the sum, is equal to zero. The paradox is that the probability of such an event is zero; therefore, it is impossible to determine the value ni of where the sum becomes zero. The article proposes to consider the event consisting in the fact that some amount of error will change value within 2m limits with a confidence level of 0,954. Within the group all the sums have a limit error. These tolerances are proposed to use for the discrepancies in geodesy instead of 2m*SQL(ni). The concept of “the law of the truncated normal distribution with Δpred = 2m” is suggested to be introduced.

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