Goodness-of-fit based confidence intervals for estimates of the size of a closed population

1984 ◽  
Vol 3 (3) ◽  
pp. 287-291 ◽  
Author(s):  
Ronald R. Regal ◽  
Ernest B. Hook
Keyword(s):  
Confidence Intervals ◽  
Goodness Of Fit ◽  
Closed Population

scholarly journals Fitting a logistic growth model to yield traits of lettuce cultivars growing in summer

2020 ◽  
Vol 14 (1) ◽  
Author(s):  
Fernanda Carini ◽  
Alberto Cargnelutti-Filho ◽  
Jéssica Maronez De Souza ◽  
Rafael Vieira Pezzini ◽  
Cassiane Ubessi ◽  
...  
Keyword(s):  
Confidence Intervals ◽  
Growth Model ◽  
Iterative Process ◽  
Logistic Model ◽  
Goodness Of Fit ◽  
Least Squares Method ◽  
Logistic Growth ◽  
Model Parameters ◽  
Yield Traits ◽  
Logistic Growth Model

The objective of this study was to fit a logistic model to fresh and dry matters of leaves and fresh and dry matters of shoots of four lettuce cultivars to describe growth in summer. Cultivars Crocantela, Elisa, Rubinela, and Vera were evaluated in the summer of 2017 and 2018, in soil in protected environment and in soilless system. Seven days after transplantation, fresh and dry leaf matters and fresh and dry shoot matters of 8 plants were weighed every 4 days. The model parameters were estimated using the software R, using the least squares method and iterative process of Gauss-Newton. We also estimated the confidence intervals of the parameters, verified the assumptions of the models, calculated the goodness-of-fit measures and the critical points, and quantified the parametric and intrinsic nonlinearities. The logistic growth model fitted well to fresh and dry leaf and shoot matters of cultivars Crocantela, Elisa, Rubinela, and Vera and is indicated to describe the growth of lettuce.

scholarly journals Design impact and significance of non-stationarity of variance in extreme rainfall

2015 ◽  
Vol 371 ◽  
pp. 117-123 ◽  
Author(s):  
M. Al Saji ◽  
J. J. O'Sullivan ◽  
A. O'Connor
Keyword(s):  
Confidence Intervals ◽  
Goodness Of Fit ◽  
Daily Rainfall ◽  
Trend Detection ◽  
Climate Change Signal ◽  
Annual Maximum ◽  
Important Indicator ◽  
Detection Techniques ◽  
The Mean ◽  
The Impact

Abstract. Stationarity in hydro-meteorological records is often investigated through an assessment of the mean value of the tested parameter. This is arguably insufficient for capturing fully the non-stationarity signal, and parameter variance is an equally important indicator. This study applied the Mann-Kendall linear and Mann-Whitney-Wilcoxon step change trend detection techniques to investigate the changes in the mean and variance of annual maximum daily rainfalls at eight stations in Dublin, Ireland, where long and high quality daily rainfall records were available. The eight stations are located in a geographically similar and spatially compact region (< 950 km2) and their rainfalls were shown to be well correlated. Results indicate that while significant positive step changes were observed in mean annual maximum daily rainfalls (1961 and 1997) at only two of the eight stations, a significant and consistent shift in the variance was observed at all eight stations during the 1980's. This period saw a widely noted positive shift in the winter North Atlantic Oscillation that greatly influences rainfall patterns in Northern Europe. Design estimates were obtained from a frequency analysis of annual maximum daily rainfalls (AM series) using the Generalised Extreme Value distribution, identified through application of the Modified Anderson Darling Goodness of Fit criterion. To evaluate the impact of the observed non-stationarity in variance on rainfall design estimates, two sets of depth-frequency relationships at each station for return periods from 5 to 100-years were constructed. The first was constructed with bootstrapped confidence intervals based on the full AM series assuming stationarity and the second was based on a partial AM series commencing in the year that followed the observed shift in variance. Confidence intervals distinguish climate signals from natural variability. Increases in design daily rainfall estimates obtained from the depth-frequency relationship developed from the truncated AM series, as opposed to those using the full series, ranged from 5 to 16% for the 5-year event and from 20 to 41% for the 100-year event. Results indicate that the observed trends exceed the envelopes of natural climate variability and suggest that the non-stationarity in variance is associated with a climate change signal. Results also illustrate the importance of considering trends in higher order moments (e.g. variance) of hydro-meteorological variables in assessing non-stationarity influences.

Factorizations of the residual likelihood criterion in discriminant analysis

1966 ◽  
Vol 62 (4) ◽  
pp. 743-752 ◽  
Author(s):  
J. Radcliffe
Keyword(s):  
Discriminant Analysis ◽  
Confidence Intervals ◽  
Goodness Of Fit ◽  
Discriminant Functions ◽  
Approximate Factorization ◽  
Analytic Proof ◽  
Independent Variables ◽  
Canonical Variables ◽  
Residual Likelihood ◽  
The Difference

Certain exact tests were developed by Williams (1952) to deal with the goodness of fit of a single hypothetical discriminant function. Bartlett (1951) generalized these results by the use of the geometric method to any number of dependent and independent variables. Bartlett's paper is divided into two parts. The first deals with an approximate factorization of the residual likelihood criterion into an effect due to the difference between the hypothetical and sample functions, and an effect due to non-collinearity. A method is given for constructing confidence intervals from the first factor. The second part of the paper gives two possible exact factorizations of the likelihood criterion, expressing the results in terms of the sample canonical variables. Kshirsagar (1964a) has expressed these results in terms of the original variables and given an analytic proof of the distribution of the factors. Williams (1955, 1961) has outlined a generalization of these results to several discriminant functions and given the result for one of the possible factorizations.

Review of Probability Distributions

2018 ◽  
pp. 25-73
Keyword(s):  
Confidence Intervals ◽  
Goodness Of Fit ◽  
Probability Distributions ◽  
Discrete Distributions ◽  
Continuous Distributions ◽  
R Language ◽  
Goodness Of Fit Tests ◽  
Anderson Darling ◽  
Analysis And Study ◽  
Waiting Lines

In Chapter 2, probability distributions are presented; the distributions exposed are those with more relation to the analysis and study of waiting lines; discrete distributions: binomial, geometric, Poisson; continuous distributions: uniform, exponential, erlang, and normal. Confidence intervals are calculated for some of the parameters of the distributions. A brief example of the generation of pseudorandom exponential times using a spreadsheet is presented. The chapter closes with the goodness-of-fit tests of probability distributions, especially the Anderson-Darling test. The statistical language of programming R is used in the exercises performed. Several codes are proposed in R Language to perform calculations automatically.

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