Approximate Confidence Intervals for the Log-Normal Standard Deviation

2015 ◽  
Vol 32 (2) ◽  
pp. 715-725 ◽  
Author(s):  
Shuhan Tang ◽  
Arthur B. Yeh
Keyword(s):  
Standard Deviation ◽  
Confidence Intervals ◽  
Approximate Confidence Intervals ◽  
Log Normal ◽  
Normal Standard

Improved approximate confidence intervals for the mean of a log-normal random variable

2002 ◽  
Vol 21 (10) ◽  
pp. 1443-1459 ◽  
Author(s):  
Douglas J. Taylor ◽  
Lawrence L. Kupper ◽  
Keith E. Muller
Keyword(s):  
Confidence Intervals ◽  
Random Variable ◽  
Normal Random Variable ◽  
The Mean ◽  
Approximate Confidence Intervals ◽  
Log Normal

scholarly journals Confidence intervals for the common coefficient of variation of rainfall in Thailand

PeerJ ◽  
2020 ◽  
Vol 8 ◽  
pp. e10004
Author(s):  
Warisa Thangjai ◽  
Sa-Aat Niwitpong ◽  
Suparat Niwitpong
Keyword(s):  
Standard Deviation ◽  
Confidence Interval ◽  
Confidence Intervals ◽  
Coefficient Of Variation ◽  
Daily Rainfall ◽  
Moisture Index ◽  
Interval Estimates ◽  
The Common ◽  
Log Normal ◽  
Confidence Interval Estimates

The log-normal distribution is often used to analyze environmental data like daily rainfall amounts. The rainfall is of interest in Thailand because high variable climates can lead to periodic water stress and scarcity. The mean, standard deviation or coefficient of variation of the rainfall in the area is usually estimated. The climate moisture index is the ratio of plant water demand to precipitation. The climate moisture index should use the coefficient of variation instead of the standard deviation for comparison between areas with widely different means. The larger coefficient of variation indicates greater dispersion, whereas the lower coefficient of variation indicates the lower risk. The common coefficient of variation, is the weighted coefficients of variation based on k areas, presents the average daily rainfall. Therefore, the common coefficient of variation is used to describe overall water problems of k areas. In this paper, we propose four novel approaches for the confidence interval estimation of the common coefficient of variation of log-normal distributions based on the fiducial generalized confidence interval (FGCI), method of variance estimates recovery (MOVER), computational, and Bayesian approaches. A Monte Carlo simulation was used to evaluate the coverage probabilities and average lengths of the confidence intervals. In terms of coverage probability, the results show that the FGCI approach provided the best confidence interval estimates for most cases except for when the sample case was equal to six populations (k = 6) and the sample sizes were small (nI < 50), for which the MOVER confidence interval estimates were the best. The efficacies of the proposed approaches are illustrated with example using real-life daily rainfall datasets from regions of Thailand.

CONFIDENCE INTERVALS FOR PROBABILITIES OF EXCEEDING THRESHOLD LIMITS WITH CENSORED LOG-NORMAL DATA

1996 ◽  
Vol 7 (3) ◽  
pp. 247-259 ◽  
Author(s):  
PASCAL WILD ◽  
REMY HORDAN ◽  
ANTOINE LEPLAY ◽  
RAYMOND VINCENT
Keyword(s):  
Confidence Intervals ◽  
Log Normal

15. Quantitative Analysis: Description and Inference

2020 ◽  
pp. 393-421
Author(s):  
Sandra Halperin ◽  
Oliver Heath
Keyword(s):  
Quantitative Analysis ◽  
Standard Deviation ◽  
Confidence Intervals ◽  
Quantitative Research ◽  
Building Blocks ◽  
Descriptive Statistics ◽  
Central Tendency ◽  
Margin Of Error ◽  
Univariate Statistics ◽  
The Mean

This chapter deals with quantitative analysis, and especially description and inference. It introduces the reader to the principles of quantitative research and offers a step-by-step guide on how to use and interpret a range of commonly used techniques. The first part of the chapter considers the building blocks of quantitative analysis, with particular emphasis on different ways of summarizing data, both graphically and with tables, and ways of describing the distribution of one variable using univariate statistics. Two important measures are discussed: the mean and the standard deviation. After elaborating on descriptive statistics, the chapter explores inferential statistics and explains how to make generalizations. It also presents the concept of confidence intervals, more commonly known as the margin of error, and measures of central tendency.

scholarly journals Robust Confidence Intervals for PM2.5 Concentration Measurements in the Ecuadorian Park La Carolina

Sensors ◽  
2020 ◽  
Vol 20 (3) ◽  
pp. 654 ◽  
Author(s):  
Wilmar Hernandez ◽  
Alfredo Mendez ◽  
Rasa Zalakeviciute ◽  
Angela Maria Diaz-Marquez
Keyword(s):  
Air Pollution ◽  
Standard Deviation ◽  
Confidence Intervals ◽  
Quality Index ◽  
Urban Park ◽  
Absolute Deviation ◽  
The Mean ◽  
Concentration Measurements ◽  
Pm2.5 Concentration

In this article, robust confidence intervals for PM2.5 (particles with size less than or equal to 2.5   μ m ) concentration measurements performed in La Carolina Park, Quito, Ecuador, have been built. Different techniques have been applied for the construction of the confidence intervals, and routes around the park and through the middle of it have been used to build the confidence intervals and classify this urban park in accordance with categories established by the Quito air quality index. These intervals have been based on the following estimators: the mean and standard deviation, median and median absolute deviation, median and semi interquartile range, a -trimmed mean and Winsorized standard error of order a , location and scale estimators based on the Andrew’s wave, biweight location and scale estimators, and estimators based on the bootstrap- t method. The results of the classification of the park and its surrounding streets showed that, in terms of air pollution by PM2.5, the park is not at caution levels. The results of the classification of the routes that were followed through the park and its surrounding streets showed that, in terms of air pollution by PM2.5, these routes are at either desirable, acceptable or caution levels. Therefore, this urban park is actually removing or attenuating unwanted PM2.5 concentration measurements.

Approximate Confidence Intervals for Estimates of Redundancy Between Sets of Variables

1989 ◽  
Vol 24 (3) ◽  
pp. 307-333 ◽  
Author(s):  
Zarrel V. Lambert ◽  
Albert R. Wildt ◽  
Richard M. Durand
Keyword(s):  
Confidence Intervals ◽  
Approximate Confidence Intervals
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