Likelihood-based confidence intervals of relative fitness for a common experimental design

2005 ◽  
Vol 62 (3) ◽  
pp. 693-699 ◽  
Author(s):  
Steven T Kalinowski ◽  
Mark L Taper
Keyword(s):  
Maximum Likelihood ◽  
Experimental Design ◽  
Confidence Intervals ◽  
Maximum Likelihood Estimates ◽  
Relative Fitness ◽  
Literature Analysis ◽  
Confidence Limits ◽  
Sample Sizes ◽  
Statistical Inferences ◽  
Different Types

Statistical inferences concerning the relative fitness of different types of individuals in a population have not been well developed. We present a method for calculating confidence intervals for maximum likelihood estimates of relative fitness obtained from an experimental design that is common in the fisheries literature. Analysis and simulation show that these confidence limits are reliable. We also show that the bias of the estimates is low for realistic sample sizes.

scholarly journals Confidence and coverage for Bland–Altman limits of agreement and their approximate confidence intervals

2016 ◽  
Vol 27 (5) ◽  
pp. 1559-1574 ◽  
Author(s):  
Andrew Carkeet ◽  
Yee Teng Goh
Keyword(s):  
Confidence Intervals ◽  
Small Sample ◽  
Interval Methods ◽  
Tolerance Interval ◽  
Confidence Limits ◽  
Sample Sizes ◽  
Limits Of Agreement ◽  
Approximate Methods ◽  
Exact Confidence Intervals ◽  
Tolerance Factors

Bland and Altman described approximate methods in 1986 and 1999 for calculating confidence limits for their 95% limits of agreement, approximations which assume large subject numbers. In this paper, these approximations are compared with exact confidence intervals calculated using two-sided tolerance intervals for a normal distribution. The approximations are compared in terms of the tolerance factors themselves but also in terms of the exact confidence limits and the exact limits of agreement coverage corresponding to the approximate confidence interval methods. Using similar methods the 50th percentile of the tolerance interval are compared with the k values of 1.96 and 2, which Bland and Altman used to define limits of agreements (i.e. [Formula: see text]+/− 1.96Sd and [Formula: see text]+/− 2Sd). For limits of agreement outer confidence intervals, Bland and Altman’s approximations are too permissive for sample sizes <40 (1999 approximation) and <76 (1986 approximation). For inner confidence limits the approximations are poorer, being permissive for sample sizes of <490 (1986 approximation) and all practical sample sizes (1999 approximation). Exact confidence intervals for 95% limits of agreements, based on two-sided tolerance factors, can be calculated easily based on tables and should be used in preference to the approximate methods, especially for small sample sizes.

Infinite Parameter Estimates in Logistic Regression: Opportunities, Not Problems

2002 ◽  
Vol 27 (2) ◽  
pp. 147-161 ◽  
Author(s):  
David Rindskopf
Keyword(s):  
Logistic Regression ◽  
Maximum Likelihood ◽  
Confidence Intervals ◽  
Maximum Likelihood Estimates ◽  
Parameter Estimates ◽  
Strict Sense ◽  
Hypothesis Tests ◽  
Infinite Slope ◽  
Alternative Method

Infinite parameter estimates in logistic regression are commonly thought of as a problem. This article shows that in principle an analyst should be happy to have an infinite slope in logistic regression, because it indicates that a predictor is perfect. Using simple approaches, hypothesis tests may be performed and confidence intervals calculated even when a slope is infinite. Some functions of parameters that are infinite are still well defined, and reasonable estimates of these quantities (in particular, LD50) may be obtained even when the maximum likelihood estimates do not, in a strict sense, exist. Surprisingly, these techniques can provide more reasonable and useful results than the most popular alternative method, exact logistic regression.

A Selected Review of Risk Models: One Hit, Multihit, Multistage, Probit, Weibull, and Pharmacokinetic

1985 ◽  
Vol 4 (4) ◽  
pp. 271-278 ◽  
Author(s):  
B. Hanes ◽  
T. Wedel
Keyword(s):  
Maximum Likelihood ◽  
Risk Model ◽  
Maximum Likelihood Estimates ◽  
Model Parameters ◽  
Confidence Limits ◽  
Risk Models ◽  
Sufficient Detail ◽  
The One

This paper provides some of the underlying mathematical derivations for the one-hit, multihit, multistage, Weibull, and pharmacokinetic risk models. Our purposes are to remove for the nonmathematician some of the mystery as to the derivation of the formulas for each particular risk model and to discuss some of the assumptions contained in the risk models. Confidence limits and maximum likelihood estimates of the model parameters are not discussed, since they are not pertinent to our objectives. Rai and Van Ryzin(1) have outlined these procedures in sufficient detail.

scholarly journals The construction of confidence intervals for frequency analysis using resampling techniques: a supplementary note

2004 ◽  
Vol 8 (6) ◽  
pp. 1174-1178 ◽  
Author(s):  
H. F. P. van den Boogaard ◽  
M. J. Hall
Keyword(s):  
Weibull Distribution ◽  
Confidence Intervals ◽  
Frequency Analysis ◽  
Likelihood Method ◽  
Bootstrap Resampling ◽  
Confidence Limits ◽  
Sample Sizes ◽  
Recent Contribution ◽  
Percentile Method ◽  
Coverage Rates

Abstract. In a recent contribution, Hall et al. (2004) examined the use of the Bootstrap resampling technique as a means of constructing confidence limits for the quantiles of the (two-parameter) Gumbel and the (three-parameter) Weibull distributions. Particular emphasis was placed on the behaviour of sample sizes of the order of 30, which are typical of those encountered in hydrological frequency analysis. The resampled confidence limits obtained for the Gumbel distribution were found to be comparable with those based upon a well-known theoretical approximation. However, those for samples of size 30 from the Weibull distribution were shown to be more problematical, with the results dependent upon the skewnesses of the resampled distributional parameters. For a further and more quantitative assessment of the suitability of Bootstrap resampling for constructing confidence intervals, so-called coverage rates were evaluated for the Weibull distribution in a supplementary study. The results show a satisfactory performance when using the percentile method but do not really mitigate the conclusion of the original study that resampled confidence limits should be employed with caution when sample sizes are of the order of 30. Keywords: Bootstrap, Jack-knife, frequency analysis, maximum likelihood method, maximum product of spacings method, confidence intervals, coverage rates

scholarly journals The Type I Generalized Half-Logistic Distribution Based on Upper Record Values

2015 ◽  
Vol 2015 ◽  
pp. 1-11 ◽  
Author(s):  
Devendra Kumar ◽  
Neetu Jain ◽  
Shivani Gupta
Keyword(s):  
Maximum Likelihood ◽  
Confidence Intervals ◽  
Record Values ◽  
Maximum Likelihood Estimates ◽  
Logistic Distribution ◽  
Type I ◽  
Special Cases ◽  
Upper Record Values ◽  
Upper Record ◽  
First Four Moments

We consider the type I generalized half-logistic distribution and derive some new explicit expressions and recurrence relations for marginal and joint moment generating functions of upper record values. Here we show the computations for the first four moments and their variances. Next we show that results for record values of this distribution can be derived from our results as special cases. We obtain the characterization result of this distribution on using the recurrence relation for single moment and conditional expectation of upper record values. We obtain the maximum likelihood estimators of upper record values and their confidence intervals. Also, we compute the maximum likelihood estimates of the parameters of upper record values and their confidence intervals. At last, we present one real case data study to emphasize the results of this paper.

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