A comparison of gamma and lognormal maximum likelihood estimators in a sequential population analysis

2001 ◽  
Vol 58 (3) ◽  
pp. 560-567 ◽  
Author(s):  
Noel G Cadigan ◽  
Ransom A Myers
Keyword(s):  
Maximum Likelihood ◽  
Population Analysis ◽  
Maximum Likelihood Estimators ◽  
Fish Populations ◽  
Population Abundance ◽  
Catch Per Unit Effort ◽  
Gamma Model ◽  
Commercial Catch ◽  
Stock Size ◽  
Gamma Distributions

We analyze the model used to assess most major commercial marine fish populations, namely, sequential population analysis (SPA). This model estimates population abundance by combining catch-at-age data with research surveys or commercial catch per unit effort indices of abundance. We examine two maximum likelihood estimators of SPA parameters. These estimators are based on assuming that the stock-size indices are from lognormal or gamma distributions. Using simulations, we find that both types of estimators can have significant biases; however, our results indicate that it is preferable to use the gamma model, because it tends to have lower bias and variability, even when the true distribution of the stock-size indices is lognormal.

Estimating trends in fishing mortality at age and length directly from research survey and commercial catch data

1998 ◽  
Vol 55 (5) ◽  
pp. 1248-1263 ◽  
Author(s):  
Alan F Sinclair
Keyword(s):  
Population Analysis ◽  
New Method ◽  
Natural Mortality ◽  
Population Abundance ◽  
Similar Magnitude ◽  
Fishing Mortality ◽  
Commercial Catch ◽  
Relative Population ◽  
Research Survey

Relative fishing mortality (R) is estimated directly as the ratio of commercial catch divided by a research vessel survey index of relative population abundance. If the survey is conducted near the middle of the fishing year, its catchability is constant, and the rate of catch reporting remains constant, R will be proportional to the actual fishing mortality (F). Trends in R will reflect trends in F. A case study is presented where R at age and length are compared with estimates obtained with sequential population analysis (SPA). They were found to be of similar magnitude and trend. This new method would be useful for stocks where SPA is not possible. It would also be a useful addition to analytical assessments where SPA is used; it provides estimates of relative F at length, it is insensitive to changes in natural mortality provided the research survey occurs close to the middle of the fishing year, and it provides useful diagnostics for interpreting SPA results.

Using Approximation Non-Bayesian Computation with Fuzzy Data to Estimation Inverse Weibull Parameters and Reliability Function

2018 ◽  
pp. 397
Author(s):  
Nadia Hashim Al-Noor ◽  
Shurooq A.K. Al-Sultany
Keyword(s):  
Maximum Likelihood ◽  
Expectation Maximization ◽  
Mean Squared Error ◽  
Maximum Likelihood Estimators ◽  
Reliability Function ◽  
Fuzzy Data ◽  
Monte Carlo Simulation Study ◽  
Weibull Parameters ◽  
Squared Error ◽  
Newton Raphson

        In real situations all observations and measurements are not exact numbers but more or less non-exact, also called fuzzy. So, in this paper, we use approximate non-Bayesian computational methods to estimate inverse Weibull parameters and reliability function with fuzzy data. The maximum likelihood and moment estimations are obtained as non-Bayesian estimation. The maximum likelihood estimators have been derived numerically based on two iterative techniques namely “Newton-Raphson” and the “Expectation-Maximization” techniques. In addition, we provide compared numerically through Monte-Carlo simulation study to obtained estimates of the parameters and reliability function in terms of their mean squared error values and integrated mean squared error values respectively.

Inference on P(Y

2020 ◽  
Vol 72 (2) ◽  
pp. 89-110
Author(s):  
Manoj Chacko ◽  
Shiny Mathew
Keyword(s):  
Maximum Likelihood ◽  
Pareto Distribution ◽  
Generalized Pareto Distribution ◽  
Maximum Likelihood Estimators ◽  
Record Values ◽  
Asymptotic Distributions ◽  
Bayes Estimators ◽  
Generalized Pareto ◽  
Pareto Distributions ◽  
Generalized Pareto Distributions

In this article, the estimation of [Formula: see text] is considered when [Formula: see text] and [Formula: see text] are two independent generalized Pareto distributions. The maximum likelihood estimators and Bayes estimators of [Formula: see text] are obtained based on record values. The Asymptotic distributions are also obtained together with the corresponding confidence interval of [Formula: see text]. AMS 2000 subject classification: 90B25

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