scholarly journals Confidence Intervals in Official Statistics: The Case of Lithuania

2012 ◽  
Vol 51 (1) ◽  
pp. 17-21
Author(s):  
Andrius Čiginas
Keyword(s):  
Normal Distribution ◽  
Confidence Intervals ◽  
Edgeworth Expansion ◽  
Normal Approximation ◽  
Official Statistics ◽  
Statistical Surveys

In the paper, the application of confidence intervals in the surveys of official statistics is discussed. It is noticedthat there are situations where at the first sight natural normal distribution-based confidence intervals are not suitable. Wedemonstrate it by examples taken from Lithuanian statistical surveys. We also discuss an Edgeworth expansion and abootstrap method as an alternative to the normal approximation.

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.

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.

Combining kNN Imputation and Bootstrap Calibrated

2010 ◽  
Vol 6 (4) ◽  
pp. 61-73 ◽  
Author(s):  
Yongsong Qin ◽  
Shichao Zhang ◽  
Chengqi Zhang
Keyword(s):  
Confidence Intervals ◽  
Incomplete Data ◽  
Asymptotic Theory ◽  
Nearest Neighbor ◽  
Normal Approximation ◽  
Simple Procedure ◽  
Important Research ◽  
K Nearest Neighbor ◽  
Research Topics ◽  
Data Discovery

The k-nearest neighbor (kNN) imputation, as one of the most important research topics in incomplete data discovery, has been developed with great successes on industrial data. However, it is difficult to obtain a mathematical valid and simple procedure to construct confidence intervals for evaluating the imputed data. This paper studies a new estimation for missing (or incomplete) data that is a combination of the kNN imputation and bootstrap calibrated EL (Empirical Likelihood). The combination not only releases the burden of seeking a mathematical valid asymptotic theory for the kNN imputation, but also inherits the advantages of the EL method compared to the normal approximation method. Simulation results demonstrate that the bootstrap calibrated EL method performs quite well in estimating confidence intervals for the imputed data with kNN imputation method.

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 A refinement of normal approximation to Poisson binomial

2005 ◽  
Vol 2005 (5) ◽  
pp. 717-728 ◽  
Author(s):  
K. Neammanee
Keyword(s):  
Normal Distribution ◽  
Normal Approximation ◽  
Random Variables ◽  
Random Variable ◽  
Standard Normal Distribution ◽  
Bernoulli Random Variables ◽  
Binomial Random Variable ◽  
Standard Normal ◽  
Correction Terms ◽  
Better Than

LetX1,X2,…,Xnbe independent Bernoulli random variables withP(Xj=1)=1−P(Xj=0)=pjand letSn:=X1+X2+⋯+Xn.Snis called a Poisson binomial random variable and it is well known that the distribution of a Poisson binomial random variable can be approximated by the standard normal distribution. In this paper, we use Taylor's formula to improve the approximation by adding some correction terms. Our result is better than before and is of order1/nin the casep1=p2=⋯=pn.

scholarly journals Growth Estimators and Confidence Intervals for the Mean of Negative Binomial Random Variables with Unknown Dispersion

2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
David Shilane ◽  
Derek Bean
Keyword(s):  
Confidence Intervals ◽  
Negative Binomial ◽  
Normal Approximation ◽  
Tail Probability ◽  
Expected Value ◽  
Alternative Methods ◽  
High Dispersion ◽  
Chi Square ◽  
Sample Mean ◽  
Wide Range

The negative binomial distribution becomes highly skewed under extreme dispersion. Even at moderately large sample sizes, the sample mean exhibits a heavy right tail. The standard normal approximation often does not provide adequate inferences about the data's expected value in this setting. In previous work, we have examined alternative methods of generating confidence intervals for the expected value. These methods were based upon Gamma and Chi Square approximations or tail probability bounds such as Bernstein's inequality. We now propose growth estimators of the negative binomial mean. Under high dispersion, zero values are likely to be overrepresented in the data. A growth estimator constructs a normal-style confidence interval by effectively removing a small, predetermined number of zeros from the data. We propose growth estimators based upon multiplicative adjustments of the sample mean and direct removal of zeros from the sample. These methods do not require estimating the nuisance dispersion parameter. We will demonstrate that the growth estimators' confidence intervals provide improved coverage over a wide range of parameter values and asymptotically converge to the sample mean. Interestingly, the proposed methods succeed despite adding both bias and variance to the normal approximation.

Sign in / Sign up

Export Citation Format

Share Document