Constructing a confidence interval for the ratio of normal distribution quantiles

2020 ◽  
Vol 26 (4) ◽  
pp. 325-334
Author(s):  
Ahad Malekzadeh ◽  
Seyed Mahdi Mahmoudi
Keyword(s):  
Confidence Interval ◽  
Normal Distribution ◽  
Confidence Intervals ◽  
Pivotal Quantity ◽  
Simple Method ◽  
Normal Populations ◽  
Generalized Pivotal Quantity ◽  
Variance Estimate

AbstractIn this paper, to construct a confidence interval (general and shortest) for quantiles of normal distribution in one population, we present a pivotal quantity that has non-central t distribution. In the case of two independent normal populations, we propose a confidence interval for the ratio of quantiles based on the generalized pivotal quantity, and we introduce a simple method for extracting its percentiles, based on which a shorter confidence interval can be created. Also, we provide general and shorter confidence intervals using the method of variance estimate recovery. The performance of five proposed methods will be examined by using simulation and examples.

scholarly journals The Shortest Confidence Interval for the Mean of a Normal Distribution

2018 ◽  
Vol 7 (2) ◽  
pp. 33
Author(s):  
Traoré Boubakar ◽  
Diabaté Lassina ◽  
Touré Belco ◽  
Fané Abdou
Keyword(s):  
Confidence Interval ◽  
Normal Distribution ◽  
Confidence Intervals ◽  
Mathematical Statistics ◽  
Standard Normal Distribution ◽  
Pivotal Quantity ◽  
Construction Technique ◽  
Standard Normal ◽  
The Mean ◽  
Shortest Confidence Intervals

An interesting topic in mathematical statistics is that of the construction of the confidence intervals. Two kinds of intervals which are both based on the method of pivotal quantity are the shortest confidence interval and the equal tail confidence intervals. The aim of this paper is to clarify and comment on the finding of such intervals and to investigation the relation between the two kinds of intervals. In particular, we will give a construction technique of the shortest confidence intervals for the mean of the standard normal distribution. Examples illustrating the use of this technique are given.

scholarly journals Confidence Intervals for the Coefficient of Variation in a Normal Distribution with a Known Population Mean

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Wararit Panichkitkosolkul
Keyword(s):  
Confidence Interval ◽  
Normal Distribution ◽  
Confidence Intervals ◽  
Coefficient Of Variation ◽  
Coverage Probability ◽  
Normal Approximation ◽  
Monte Carlo Simulation Study ◽  
Population Mean ◽  
Expected Length ◽  
Simulation Results

This paper presents three confidence intervals for the coefficient of variation in a normal distribution with a known population mean. One of the proposed confidence intervals is based on the normal approximation. The other proposed confidence intervals are the shortest-length confidence interval and the equal-tailed confidence interval. A Monte Carlo simulation study was conducted to compare the performance of the proposed confidence intervals with the existing confidence intervals. Simulation results have shown that all three proposed confidence intervals perform well in terms of coverage probability and expected length.

scholarly journals A Bayesian Approach for Estimation of Coefficients of Variation of Normal Distributions

2021 ◽  
Vol 50 (1) ◽  
pp. 261-278
Author(s):  
Warisa Thangjai ◽  
Sa-Aat Niwitpong ◽  
Suparat Niwitpong
Keyword(s):  
Confidence Interval ◽  
Normal Distribution ◽  
Confidence Intervals ◽  
Coefficient Of Variation ◽  
Bayesian Approaches ◽  
Normal Distributions ◽  
Generalized Confidence Interval ◽  
Coefficients Of Variation ◽  
The Difference ◽  
Highest Posterior Density

The coefficient of variation is widely used as a measure of data precision. Confidence intervals for a single coefficient of variation when the data follow a normal distribution that is symmetrical and the difference between the coefficients of variation of two normal populations are considered in this paper. First, the confidence intervals for the coefficient of variation of a normal distribution are obtained with adjusted generalized confidence interval (adjusted GCI), computational, Bayesian, and two adjusted Bayesian approaches. These approaches are compared with existing ones comprising two approximately unbiased estimators, the method of variance estimates recovery (MOVER) and generalized confidence interval (GCI). Second, the confidence intervals for the difference between the coefficients of variation of two normal distributions are proposed using the same approaches, the performances of which are then compared with the existing approaches. The highest posterior density interval was used to estimate the Bayesian confidence interval. Monte Carlo simulation was used to assess the performance of the confidence intervals. The results of the simulation studies demonstrate that the Bayesian and two adjusted Bayesian approaches were more accurate and better than the others in terms of coverage probabilities and average lengths in both scenarios. Finally, the performances of all of the approaches for both scenarios are illustrated via an empirical study with two real-data examples.

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.

Verification of the Calculation Assumptions Applied to Solutions of the Acoustic Measurements Uncertainty

2015 ◽  
Vol 39 (2) ◽  
pp. 199-202
Author(s):  
Wojciech Batko ◽  
Renata Bal
Keyword(s):  
Normal Distribution ◽  
Confidence Intervals ◽  
Uncertainty Of Measurement ◽  
Acoustic Measurements ◽  
Uncertainty In Measurement ◽  
Sound Levels ◽  
Measurement Results ◽  
Analysis Of Results ◽  
Essential Problem ◽  
Expression Of Uncertainty

Abstract The assessment of the uncertainty of measurement results, an essential problem in environmental acoustic investigations, is undertaken in the paper. An attention is drawn to the - usually omitted - problem of the verification of assumptions related to using the classic methods of the confidence intervals estimation, for the controlled measuring quantity. Especially the paper directs attention to the need of the verification of the assumption of the normal distribution of the measuring quantity set, being the base for the existing and binding procedures of the acoustic measurements assessment uncertainty. The essence of the undertaken problem concerns the binding legal and standard acts related to acoustic measurements and recommended in: 'Guide to the expression of uncertainty in measurement' (GUM) (OIML 1993), developed under the aegis of the International Bureau of Measures (BIPM). The model legitimacy of the hypothesis of the normal distribution of the measuring quantity set in acoustic measurements is discussed and supplemented by testing its likelihood on the environment acoustic results. The Jarque-Bery test based on skewness and flattening (curtosis) distribution measures was used for the analysis of results verifying the assumption. This test allows for the simultaneous analysis of the deviation from the normal distribution caused both by its skewness and flattening. The performed experiments concerned analyses of the distribution of sound levels: LD, LE, LN, LDWN, being the basic noise indicators in assessments of the environment acoustic hazards.

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.

Empirical Nonparametric Bootstrap Strategies in Quantitative Trait Loci Mapping: Conditioning on the Genetic Model

Genetics ◽  
1998 ◽  
Vol 148 (1) ◽  
pp. 525-535
Author(s):  
Claude M Lebreton ◽  
Peter M Visscher
Keyword(s):  
Quantitative Trait Loci ◽  
Confidence Interval ◽  
Confidence Intervals ◽  
Quantitative Trait ◽  
Genetic Factors ◽  
Genetic Model ◽  
Original Data ◽  
Nonparametric Bootstrap ◽  
Test Protocol ◽  
Trait Loci

AbstractSeveral nonparametric bootstrap methods are tested to obtain better confidence intervals for the quantitative trait loci (QTL) positions, i.e., with minimal width and unbiased coverage probability. Two selective resampling schemes are proposed as a means of conditioning the bootstrap on the number of genetic factors in our model inferred from the original data. The selection is based on criteria related to the estimated number of genetic factors, and only the retained bootstrapped samples will contribute a value to the empirically estimated distribution of the QTL position estimate. These schemes are compared with a nonselective scheme across a range of simple configurations of one QTL on a one-chromosome genome. In particular, the effect of the chromosome length and the relative position of the QTL are examined for a given experimental power, which determines the confidence interval size. With the test protocol used, it appears that the selective resampling schemes are either unbiased or least biased when the QTL is situated near the middle of the chromosome. When the QTL is closer to one end, the likelihood curve of its position along the chromosome becomes truncated, and the nonselective scheme then performs better inasmuch as the percentage of estimated confidence intervals that actually contain the real QTL's position is closer to expectation. The nonselective method, however, produces larger confidence intervals. Hence, we advocate use of the selective methods, regardless of the QTL position along the chromosome (to reduce confidence interval sizes), but we leave the problem open as to how the method should be altered to take into account the bias of the original estimate of the QTL's position.

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