A New Approach to Estimating Populations by the Removal Method

1983 ◽  
Vol 40 (12) ◽  
pp. 2153-2169 ◽  
Author(s):  
Jon Schnute
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
New Brunswick ◽  
Population Size ◽  
Confidence Intervals ◽  
Likelihood Estimation ◽  
Data Interpretation ◽  
Population Estimate ◽  
New Approach ◽  
Removal Method

This paper presents a new approach to the use of removal data in estimating the size of a population of fish or other animals. The theory admits a variety of assumptions on how catchability varies among fishings including the assumption of constant catchability, which underlies most previous work. The methods here hinge on maximum likelihood estimation, and they can be used both to decide objectively if the data justify rejecting constant catchability and to determine confidence intervals for the parameters. The work includes a new method of assigning confidence to the population estimate and points out problems with methods currently available in the literature, even in the case of constant catchability. The theory is applied both to data in historical literature and to more recent data from streams in New Brunswick, Canada. These examples demonstrate that the assumption of constant catchability can frequently lead to serious errors in data interpretation. In some cases, the conclusion that the population size is well known may be blatantly false, and reasonable estimates may be impossible without further data.

scholarly journals Plotting positions via maximum-likelihood for a non-standard situation

1997 ◽  
Vol 1 (2) ◽  
pp. 357-366 ◽  
Author(s):  
D. A. Jones
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Frequency Analysis ◽  
Likelihood Estimation ◽  
Similar Data ◽  
Statistical Distributions ◽  
Annual Maximum ◽  
New Approach ◽  
Special Cases ◽  
Standard Situation

Abstract. A new approach is developed for the specification of the plotting positions used in the frequency analysis of extreme flows, rainfalls or similar data. The approach is based on the concept of maximum likelihood estimation and it is applied here to provide plotting positions for a range of problems which concern non-standard versions of annual-maximum data. This range covers the inclusion of incomplete years of data and also the treatment of cases involving regional maxima, where the number of sites considered varies from year to year. These problems, together with a not-to-be-recommended approach to using historical information, can be treated as special cases of a non-standard situation in which observations arise from different statistical distributions which vary in a simple, known, way.

scholarly journals A New Generator of Probability Models: The Exponentiated Sine-G Family for Lifetime Studies

Entropy ◽  
2021 ◽  
Vol 23 (11) ◽  
pp. 1394
Author(s):  
Mustapha Muhammad ◽  
Huda M. Alshanbari ◽  
Ayed R. A. Alanzi ◽  
Lixia Liu ◽  
Waqas Sami ◽  
...  
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Confidence Intervals ◽  
Likelihood Estimation ◽  
Quantile Function ◽  
Weibull Model ◽  
Mean Square ◽  
Reliability Parameter ◽  
Coverage Probabilities ◽  
The Mean

In this article, we propose the exponentiated sine-generated family of distributions. Some important properties are demonstrated, such as the series representation of the probability density function, quantile function, moments, stress-strength reliability, and Rényi entropy. A particular member, called the exponentiated sine Weibull distribution, is highlighted; we analyze its skewness and kurtosis, moments, quantile function, residual mean and reversed mean residual life functions, order statistics, and extreme value distributions. Maximum likelihood estimation and Bayes estimation under the square error loss function are considered. Simulation studies are used to assess the techniques, and their performance gives satisfactory results as discussed by the mean square error, confidence intervals, and coverage probabilities of the estimates. The stress-strength reliability parameter of the exponentiated sine Weibull model is derived and estimated by the maximum likelihood estimation method. Also, nonparametric bootstrap techniques are used to approximate the confidence interval of the reliability parameter. A simulation is conducted to examine the mean square error, standard deviations, confidence intervals, and coverage probabilities of the reliability parameter. Finally, three real applications of the exponentiated sine Weibull model are provided. One of them considers stress-strength data.

Sign in / Sign up

Export Citation Format

Share Document