Confidence Interval for Coefficient of Variation of Inverse Gamma Distributions

2020 ◽  
pp. 407-418
Author(s):  
Theerapong Kaewprasert ◽  
Sa-Aat Niwitpong ◽  
Suparat Niwitpong
Keyword(s):  
Confidence Interval ◽  
Coefficient Of Variation ◽  
Inverse Gamma ◽  
Gamma Distributions

Interspike interval distributions of spiking neurons driven by fluctuating inputs

2011 ◽  
Vol 106 (1) ◽  
pp. 361-373 ◽  
Author(s):  
Srdjan Ostojic
Keyword(s):  
Coefficient Of Variation ◽  
Cortical Neurons ◽  
Interspike Interval ◽  
Full Range ◽  
Spiking Neurons ◽  
Neuron Models ◽  
Integrate And Fire ◽  
Gamma Distributions ◽  
Spiking Neuron Models ◽  
Analytical Tools

Interspike interval (ISI) distributions of cortical neurons exhibit a range of different shapes. Wide ISI distributions are believed to stem from a balance of excitatory and inhibitory inputs that leads to a strongly fluctuating total drive. An important question is whether the full range of experimentally observed ISI distributions can be reproduced by modulating this balance. To address this issue, we investigate the shape of the ISI distributions of spiking neuron models receiving fluctuating inputs. Using analytical tools to describe the ISI distribution of a leaky integrate-and-fire (LIF) neuron, we identify three key features: 1) the ISI distribution displays an exponential decay at long ISIs independently of the strength of the fluctuating input; 2) as the amplitude of the input fluctuations is increased, the ISI distribution evolves progressively between three types, a narrow distribution (suprathreshold input), an exponential with an effective refractory period (subthreshold but suprareset input), and a bursting exponential (subreset input); 3) the shape of the ISI distribution is approximately independent of the mean ISI and determined only by the coefficient of variation. Numerical simulations show that these features are not specific to the LIF model but are also present in the ISI distributions of the exponential integrate-and-fire model and a Hodgkin-Huxley-like model. Moreover, we observe that for a fixed mean and coefficient of variation of ISIs, the full ISI distributions of the three models are nearly identical. We conclude that the ISI distributions of spiking neurons in the presence of fluctuating inputs are well described by gamma distributions.

scholarly journals The Bayesian Confidence Interval for Coefficient of Variation of Zero-inflated Poisson Distribution with Application to Daily COVID-19 Deaths in Thailand

2021 ◽  
Vol 5 ◽  
pp. 62-76
Author(s):  
Sunisa Junnumtuam ◽  
Sa-Aat Niwitpong ◽  
Suparat Niwitpong
Keyword(s):  
Confidence Interval ◽  
Coefficient Of Variation ◽  
Average Length ◽  
Simulated Data ◽  
Posterior Density ◽  
The World ◽  
Bayesian Confidence Interval ◽  
Percentile Bootstrap ◽  
Highest Posterior Density ◽  
Better Than

Coronavirus disease 2019 (COVID-19) has spread rapidly throughout the world and has caused millions of deaths. However, the number of daily COVID-19 deaths in Thailand has been low with most daily records showing zero deaths, thereby making them fit a Zero-Inflated Poisson (ZIP) distribution. Herein, confidence intervals for the Coefficient Of Variation (CV) of a ZIP distribution are derived using four methods: the standard bootstrap (SB), percentile bootstrap (PB), Markov Chain Monte Carlo (MCMC), and the Bayesian-based highest posterior density (HPD), for which using the variance of the CV is unnecessary. We applied the methods to both simulated data and data on the number of daily COVID-19 deaths in Thailand. Both sets of results show that the SB, MCMC, and HPD methods performed better than PB for most cases in terms of coverage probability and average length. Overall, the HPD method is recommended for constructing the confidence interval for the CV of a ZIP distribution. Doi: 10.28991/esj-2021-SPER-05 Full Text: PDF

scholarly journals Three-Stage Sequential Estimation of the Inverse Coefficient of Variation of the Normal Distribution

Computation ◽  
2019 ◽  
Vol 7 (4) ◽  
pp. 69 ◽  
Author(s):  
Ali Yousef ◽  
Hosny Hamdy
Keyword(s):  
Confidence Interval ◽  
Normal Distribution ◽  
Coefficient Of Variation ◽  
Sequential Estimation ◽  
Point Estimation ◽  
Squared Error Loss Function ◽  
Fixed Sample ◽  
Sampling Cost ◽  
Better Than ◽  
Inverse Coefficient

This paper sequentially estimates the inverse coefficient of variation of the normal distribution using Hall’s three-stage procedure. We find theorems that facilitate finding a confidence interval for the inverse coefficient of variation that has pre-determined width and coverage probability. We also discuss the sensitivity of the constructed confidence interval to detect a possible shift in the inverse coefficient of variation. Finally, we find the asymptotic regret encountered in point estimation of the inverse coefficient of variation under the squared-error loss function with linear sampling cost. The asymptotic regret provides negative values, which indicate that the three-stage sampling does better than the optimal fixed sample size had the population inverse coefficient of variation been known.

scholarly journals Session-To-Session Variations of External Load Measures of Youth Soccer Players in Medium-Sided Games

2019 ◽  
Vol 16 (19) ◽  
pp. 3612
Author(s):  
Filipe Manuel Clemente ◽  
Alireza Rabbani ◽  
Mehdi Kargarfard ◽  
Pantelis Theodoros Nikolaidis ◽  
Thomas Rosemann ◽  
...  
Keyword(s):  
Confidence Interval ◽  
Coefficient Of Variation ◽  
External Load ◽  
Soccer Players ◽  
Small Decrease ◽  
Youth Soccer ◽  
Distance Range ◽  
Time Motion ◽  
Typical Error ◽  
Stable Performance

The aim of this study was to analyze the variability of time-motion variables during five vs. five games when completed within the same session as, and between, two different sessions. Ten under-19 male soccer players (18.27 ± 0.47 years old) participated in this study. The five vs. five matches (3 × 5 min) were played twice with a 3-day interval of rest in the same week. Moderate between-session variations were observed for TD (total distance) (range coefficient of variation (CV), 6.9; 8.3%, confidence interval (CI), (5.0; 14.0), standardized typical error (STE), 0.68; 1.06, (0.64; 1.75)) and RD (running distance) (range CV, 53.3; 145.7%, (36.6; 338.9), STE, 0.83; 1.09, (0.60; 1.76)). PL (player load) showed small variations (range CV, 4.9; 6.0%, [3.6; 10.1], STE, 0.37; 0.43, (0.27; 0.71)). In within-session analyses for examining the differences between sets, a small decrease was observed in RD in set 3 versus set 2 (−14.8%, 90% CI (−32.1; 6.9%); standardized difference (ES): −0.39 (0.95; 0.16)). TD decreased with moderate (−3.5%, (−6.8; −0.1%); ES: −0.65(−1.30; −0.01)) and large (−8.2%, (−11.4; −4.9%); ES: −1.58(−2.24; −0.92)) effects in sets 2 and 3, respectively, versus set 1. Our results suggest that PL is the most stable performance variable. It was also verified that measures had a progressive decreasing tendency within a session.

Confidence Intervals for the Ratio of the Coefficients of Variation of Inverse-Gamma Distributions

2021 ◽  
Author(s):  
Theerapong Kaewprasert ◽  
Sa-Aat Niwitpong ◽  
Suparat Niwitpong
Keyword(s):  
Confidence Intervals ◽  
Bayesian Method ◽  
Simulation Studies ◽  
Jeffreys Prior ◽  
Inverse Gamma ◽  
Gamma Distributions ◽  
Coefficients Of Variation ◽  
Coverage Probabilities ◽  
Percentile Bootstrap ◽  
Better Than

Herein, we present four methods for constructing confidence intervals for the ratio of the coefficients of variation of inverse-gamma distributions using the percentile bootstrap, fiducial quantities, and Bayesian methods based on the Jeffreys and uniform priors. We compared their performances using coverage probabilities and expected lengths via simulation studies. The results show that the confidence intervals constructed with the Bayesian method based on the uniform prior and fiducial quantities performed better than those constructed with the Bayesian method based on the Jeffreys prior and the percentile bootstrap. Rainfall data from Thailand was used to illustrate the efficacies of the proposed methods.

Monitoring Field Variability Using Confidence Interval for Coefficient of Variation

2008 ◽  
Vol 37 (6) ◽  
pp. 831-846 ◽  
Author(s):  
Girma Taye ◽  
Peter Njuho
Keyword(s):  
Confidence Interval ◽  
Coefficient Of Variation ◽  
Field Variability

Approximate Confidence Limits for the Coefficient of Variation of Gamma Distributions

Biometrics ◽  
1965 ◽  
Vol 21 (3) ◽  
pp. 733 ◽  
Author(s):  
H. Linhart
Keyword(s):  
Coefficient Of Variation ◽  
Confidence Limits ◽  
Gamma Distributions

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.

Spectrographic Determination of Boron in Carbon and Alloy Steels

1967 ◽  
Vol 21 (5) ◽  
pp. 277-281 ◽  
Author(s):  
C. R. Hines ◽  
J. K. Hurwitz
Keyword(s):  
Confidence Interval ◽  
Coefficient Of Variation ◽  
Counter Electrode ◽  
Spectrographic Determination ◽  
Included Angle ◽  
Alloy Steels ◽  
Spectrographic Method ◽  
Electrical Polarity

A new spectrographic method for the determination of boron in carbon and alloy steels has been developed by which accurate, precise, and rapid determinations of boron in the range 5–90 ppm are obtained. In this new procedure, a condensed overdamped discharge is used to excite the spectrum, the sample's electrical polarity is negative, and the graphite counter electrode has a pointed tip with an included angle of 15°. The repeatability of the method expressed as the coefficient of variation is ±5.8%; and at a 95% confidence interval, the spectrographic results agree with chemical determinations within ±22% of the amount present in the sample.

Sign in / Sign up

Export Citation Format

Share Document