scholarly journals Coverage versus Confidence

2021 ◽  
Vol 23 ◽  
Author(s):  
Peyton Cook
Keyword(s):  
Confidence Interval ◽  
Confidence Intervals ◽  
Negative Binomial Distribution ◽  
Binomial Distribution ◽  
Coverage Probability ◽  
Negative Binomial ◽  
Asymptotic Confidence Interval ◽  
Population Proportion ◽  
Coverage Probabilities ◽  
The Mean

This article is intended to help students understand the concept of a coverage probability involving confidence intervals. Mathematica is used as a language for describing an algorithm to compute the coverage probability for a simple confidence interval based on the binomial distribution. Then, higher-level functions are used to compute probabilities of expressions in order to obtain coverage probabilities. Several examples are presented: two confidence intervals for a population proportion based on the binomial distribution, an asymptotic confidence interval for the mean of the Poisson distribution, and an asymptotic confidence interval for a population proportion based on the negative binomial distribution.

A METHOD OF SAMPLING THE BALSAM WOOLLY APHID ON FRASER FIR IN NORTH CAROLINA

1969 ◽  
Vol 101 (8) ◽  
pp. 883-889 ◽  
Author(s):  
Gene D. Amman
Keyword(s):  
North Carolina ◽  
Normal Distribution ◽  
Negative Binomial Distribution ◽  
Binomial Distribution ◽  
Negative Binomial ◽  
Sampling Frequency ◽  
Fraser Fir ◽  
Woolly Aphid ◽  
The Mean

AbstractPopulations of the balsam woolly aphid on Fraser fir trees were sampled without replacement. Sampling frequency was based on the embryological period of the aphid at mean monthly temperatures in the field. The sample for each date consisted of 16 pieces of bark, 1/2 in. diameter, from each of 10 trees. Precision of the method was usually within ±10% of the mean. The largest proportion of variance was within trees. Stratification of samples by levels within trees decreased variance estimates.Frequency distributions of counts of most stages of the aphid approximated the negative binomial distribution. Therefore, data were transformed to logarithms in order to approximate the normal distribution.

The relationship between IgA activity against 4th-stage larvae and density-dependent effects on the number of 4th-stage larvae ofTeladorsagia circumcinctain naturally infected sheep

Parasitology ◽  
2004 ◽  
Vol 129 (3) ◽  
pp. 363-369 ◽  
Author(s):  
M. J. STEAR ◽  
K. BAIRDEN ◽  
G. T. INNOCENT ◽  
S. MITCHELL ◽  
S. STRAIN ◽  
...  
Keyword(s):  
Negative Binomial Distribution ◽  
Binomial Distribution ◽  
Negative Binomial ◽  
Infection Intensity ◽  
Intensity Of Infection ◽  
Mean Intensity ◽  
Teladorsagia Circumcincta ◽  
The Mean ◽  
Low Levels ◽  
The Relationship

The number ofTeladorsagia circumcincta4th-stage larvae in naturally infected lambs from a single farm varied among lambs and among different years. Within each year the distribution of 4th-stage larvae among lambs was similar to that expected from a negative binomial distribution. The ratio of 4th-stage larvae to adultT. circumcinctawas low in two years with a low mean intensity of infection but high in two years with a higher mean intensity of infection. The negative binomial distribution is defined by the mean and byk, a parameter that measures dispersion;kwas low when mean infection intensity was low but higher when mean infection intensity was high. Askis an inverse index of overdispersion this indicated that the distribution of 4th-stage larvae was more overdispersed at low levels of infection. In a combined analysis, the number of adultT. circumcinctaand the plasma IgA activity against 4th-stage larvae were both associated with increased numbers of 4th-stage larvae. There was a statistical interaction between the number of adults and IgA activity that moderated their combined effect.

Point Quadrat methods for the analysis of vegetation — the treatment of data for tussock grasses

1953 ◽  
Vol 1 (3) ◽  
pp. 457 ◽  
Author(s):  
DW Goodall
Keyword(s):  
Successive Approximation ◽  
Negative Binomial Distribution ◽  
Binomial Distribution ◽  
Negative Binomial ◽  
The Mean ◽  
Point Quadrat ◽  
Tussock Grasses

An improved estimate of the mean cover repetition in the centres of tussocks may be obtained by fitting a negative binomial distribution by successive approximation.

The processes influencing the distribution of parasitic nematodes among naturally infected lambs

Parasitology ◽  
1998 ◽  
Vol 117 (2) ◽  
pp. 165-171 ◽  
Author(s):  
M. J. STEAR ◽  
K. BAIRDEN ◽  
S. C. BISHOP ◽  
G. GETTINBY ◽  
Q. A. McKELLAR ◽  
...  
Keyword(s):  
Negative Binomial Distribution ◽  
Binomial Distribution ◽  
Negative Binomial ◽  
Good Description ◽  
Skewed Distribution ◽  
The Other ◽  
Host Susceptibility ◽  
Parasitic Nematodes ◽  
The Mean ◽  
The Impact

The impact of mixed, nematode infection upon a group of animals will depend upon the number of nematodes present, how they are distributed among hosts and whether individuals that are heavily parasitized with one species are more likely to be heavily parasitized with other species. A survey of over 500 six-month-old, Scottish Blackface lambs from a single farm in Southwest Strathclyde identified 7 different categories of nematodes in the abomasum and small intestine. There were considerable differences among years and among nematodes in the prevalence and mean intensity of infection. Ostertagia circumcincta was present in nearly all lambs and judged by prevalence and intensity is one of the most successful of all parasitic nematodes. Each category of nematodes had a skewed distribution; most animals had relatively few worms but a small proportion had many worms. The variances of the number of nematodes in each category were approximately equal to the square of the mean. The counts of adult O. circumcincta followed a negative binomial distribution, but the negative binomial distribution did not provide a good description of the observed values for the other species. These other species had a lower prevalence and possibly some sheep were not exposed to infection. There was no significant genetic variation among lambs in the number of nematodes present and therefore the differences among these lambs were unlikely to be a consequence of genetic differences in host susceptibility. Lambs with increased numbers of one species were more likely to have increased numbers of the other species, but the correlations were weak and may reflect covariation in exposure to different parasites.

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