Estimating spawning escapements from periodic counts: a comparison of methods

1999 ◽  
Vol 56 (5) ◽  
pp. 888-896 ◽  
Author(s):  
Ray Hilborn ◽  
Brian G Bue ◽  
Samuel Sharr
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Method ◽  
Pacific Salmon ◽  
Interpolation Method ◽  
Linear Interpolation ◽  
Likelihood Method ◽  
Estimation Methods ◽  
Data Sets ◽  
Time Model ◽  
Using Data

The escapement of Pacific salmon is often estimated by periodic counts of spawners, calculating the number of fish-days present and dividing by the average number of days a fish spends in the survey area. We present a maximum likelihood method to calculate the number of spawning fish and compare this approach with the most commonly used method, which relies on linear interpolation between observations. The maximum likelihood method is computationally more demanding; however, it does provide a statistical basis for describing uncertainty and can also be used to deal with data sets where the first or last counts are nonzero or where there are few observations. We compared escapement estimation methods using data from 18 experimental streams where the number of fish in the stream was evaluated by weir and carcass counts. In this comparison, the method of linear interpolation deviated from the weir count by an average of 19%, whereas the maximum likelihood method deviated by 23, 24, 30, or 40% depending upon which likelihood and arrival time model was used. We conclude that for most data sets where measures of uncertainty are not required, the linear interpolation method is adequate but recommend an examination of maximum likelihood methods when an estimate of uncertainty is required.

scholarly journals On Modified Burr XII-Inverse Weibull Distribution: Development, Properties, Characterizations and Applications

2020 ◽  
pp. 721-735
Author(s):  
Fiaz Ahmad Bhatti ◽  
G. G. Hamedani ◽  
Haitham M. Yousof ◽  
Azeem Ali ◽  
Munir Ahmad
Keyword(s):  
Maximum Likelihood ◽  
Hazard Rate ◽  
Maximum Likelihood Method ◽  
Real Data ◽  
Lifetime Distribution ◽  
Maximum Likelihood Estimates ◽  
Likelihood Method ◽  
Data Sets ◽  
Quarterly Earnings ◽  
Inverse Weibull Distribution

A flexible lifetime distribution with increasing, decreasing, inverted bathtub and modified bathtub hazard rate called Modified Burr XII-Inverse Weibull (MBXII-IW) is introduced and studied. The density function of MBXII-IW is exponential, left-skewed, right-skewed and symmetrical shaped.  Descriptive measures on the basis of quantiles, moments, order statistics and reliability measures are theoretically established. The MBXII-IW distribution is characterized via different techniques. Parameters of MBXII-IW distribution are estimated using maximum likelihood method. The simulation study is performed to illustrate the performance of the maximum likelihood estimates (MLEs). The potentiality of MBXII-IW distribution is demonstrated by its application to real data sets: serum-reversal times and quarterly earnings.

Application of the maximum‐likelihood method (MLM) for sonic velocity logging

Geophysics ◽  
1986 ◽  
Vol 51 (3) ◽  
pp. 780-787 ◽  
Author(s):  
Kai Hsu ◽  
Arthur B. Baggeroer
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Method ◽  
Laboratory Data ◽  
Signal Strength ◽  
Likelihood Method ◽  
Data Sets ◽  
Normalization Procedure ◽  
Computational Requirement ◽  
Full Waveforms ◽  
Schlumberger Array

Modern digital sonic tools can record full waveforms using an array of receivers. The recorded waveforms are extremely complicated because wave components overlap in time. Conventional beamforming approaches, such as semblance processing, while robust, sometimes do not resolve the interfering wave components propagating at similar speeds, such as multiple compressional arrivals due to the formation alteration surrounding the borehole. Here the maximum‐likelihood method (MLM), a high‐resolution array processing algorithm, is modified and applied to process borehole array sonic data. Extensive modifications of the original MLM algorithm were necessary because of the transient character of the sonic data and its effect upon the spectral covariance matrix. We applied MLM to several array sonic data sets, including laboratory data, synthetic waveforms, and field data taken by a Schlumberger array sonic tool. MLM’s slowness resolution is demonstrated in resolving a secondary compressional arrival from the primary compressional arrival in an altered formation, and the formation compressional arrival in the presence of a stronger casing arrival in an unbonded cased hole. In comparison with the semblance processing results, the MLM results clearly show a better slowness resolution. However, in the case of a weak formation arrival, the semblance processing tends to enhance and resolve the weak arrival by the semblance normalization procedure, while the MLM, designed to estimate the signal strength, does not. The heavy computational requirement (mainly, many matrix inversions) in the MLM makes it much slower than semblance processing, which may prohibit implementation of the MLM algorithm in a real‐time environment.

scholarly journals A New Flexible Three-Parameter Model: Properties, Clayton Copula, and Modeling Real Data

Symmetry ◽  
2020 ◽  
Vol 12 (3) ◽  
pp. 440 ◽  
Author(s):  
Abdulhakim A. Al-babtain ◽  
I. Elbatal ◽  
Haitham M. Yousof
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Method ◽  
Real Data ◽  
Likelihood Method ◽  
Model Parameters ◽  
Simple Type ◽  
Data Sets ◽  
New Model ◽  
Clayton Copula ◽  
Mathematical Properties

In this article, we introduced a new extension of the binomial-exponential 2 distribution. We discussed some of its structural mathematical properties. A simple type Copula-based construction is also presented to construct the bivariate- and multivariate-type distributions. We estimated the model parameters via the maximum likelihood method. Finally, we illustrated the importance of the new model by the study of two real data applications to show the flexibility and potentiality of the new model in modeling skewed and symmetric data sets.

scholarly journals Estimation of Critical Headway at Small Urban Roundabout

2020 ◽  
Vol 32 (1) ◽  
pp. 103-117
Author(s):  
Danijela Maslać ◽  
Dražen Cvitanić ◽  
Ivan Lovrić
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Method ◽  
Likelihood Method ◽  
Estimation Methods ◽  
Project Design ◽  
Capacity Estimation ◽  
Local Conditions ◽  
Large Numbers ◽  
The World

Before choosing an intersection project design, an important step is to examine the justification of the construction on the basis of defined criteria. One of the key criteria is the analysis of capacity. Large numbers of roundabout capacity models are present in the world, most of them adapted to the conditions of the country they originate from and they need to be calibrated for local conditions. Key parameters for calibration are critical headway and follow-up headway. Follow-up headway can be measured directly in the field, while critical headway cannot be measured, but is estimated. Many critical headway estimation methods exist (over 30) and each of them provides different values. Different values of critical headway result in different capacity estimation values. This raises the question which method provides more realistic estimations under certain conditions. In this paper, four most frequently used critical headway estimation methods (Raff, Maximum likelihood method, Wu, Logit) were selected to be tested by comparison of theoretical capacity models and actual measured capacity at a small urban roundabout.

scholarly journals Comparison of Some Methods to Fit a Multiplicative Tariff Structure to Observed Risk Data

1986 ◽  
Vol 16 (1) ◽  
pp. 63-68 ◽  
Author(s):  
B. Ajne
Keyword(s):  
Maximum Likelihood ◽  
Goodness Of Fit ◽  
Maximum Likelihood Method ◽  
Likelihood Method ◽  
Data Sets ◽  
Tariff Structure ◽  
Multiplicative Models

AbstractThree methods for fitting multiplicative models to observed, cross-classified risk data are compared. They are the method of Bailey–Simon, the method of marginal totals and a maximum likelihood method. The methods are applied to a number of risk data sets and compared with respect to balance and goodness-of-fit.

scholarly journals Inverse Lomax-Exponentiated G (IL-EG) Family of Distributions: Properties and Applications

2020 ◽  
pp. 48-64
Author(s):  
Jamilu Yunusa Falgore ◽  
Sani Ibrahim Doguwa
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Method ◽  
Moment Generating Function ◽  
Maximum Likelihood Estimates ◽  
Likelihood Method ◽  
Data Sets ◽  
Baseline Model ◽  
New Family ◽  
Family Of Distributions ◽  
Better Than

A new generator of continuous distributions called the Inverse Lomax-Exponentiated G family, which has three extra positive parameters is proposed. The structural properties of the new family that holds for any continuous baseline model including explicit density function expressions, moments, inequality measurements, moment generating function, reliability functions, Renyi and Shanon entropies, and distribution of order statistics are derived. A Monte Carlo simulation to test the efficiency of the maximum likelihood estimates is conducted. The application of the new sub-model to the two data sets using the maximum likelihood method indicates that the new model is better than the existing competitors.

scholarly journals Truncated Akash distribution: properties and applications

2020 ◽  
Vol 9 (5) ◽  
pp. 179-184
Author(s):  
Kamlesh Kumar Shukla
Keyword(s):  
Maximum Likelihood ◽  
Coefficient Of Variation ◽  
Hazard Rate ◽  
Maximum Likelihood Method ◽  
Cumulative Distribution ◽  
Likelihood Method ◽  
Data Sets ◽  
Proposed Model ◽  
Rate Functions ◽  
Mean And Variance

In this paper, Truncated Akash distribution has been proposed. Its mean and variance have been derived. Nature of cumulative distribution and hazard rate functions have been derived and presented graphically. Its moments including Coefficient of Variation, Skenwness, Kurtosis and Index of dispersion have been derived. Maximum likelihood method of estimation has been used to estimate the parameter of proposed model. It has been applied on three data sets and compares its superiority over one parameter exponential, Lindley, Akash, Ishita and truncated Lindley distribution.

scholarly journals Modified generalized marshall-olkin family of distributions

2019 ◽  
Vol 7 (1) ◽  
pp. 18
Author(s):  
Muhammad Aslam ◽  
Zawar Hussain ◽  
Zahid Asghar
Keyword(s):  
Maximum Likelihood ◽  
Goodness Of Fit ◽  
Maximum Likelihood Method ◽  
Likelihood Estimation ◽  
Likelihood Method ◽  
Model Parameters ◽  
Data Sets ◽  
Goodness Of Fit Tests ◽  
New Family ◽  
Family Of Distributions

In this article, we propose a new family of distributions using the T-X family named as modified generalized Marshall-Olkin family of distributions. Comprehensive mathematical and statistical properties of this family of distributions are provided. The model parameters are estimated by maximum likelihood method. The maximum likelihood estimation under Type-II censoring is also discussed. Two lifetime data sets are used to show the suitability and applicability of the new family of distributions. For comparison purposes, different goodness of fit tests are used.  

scholarly journals Applying Transformer Insulation Using Weibull Extended Distribution Based on Progressive Censoring Scheme

Axioms ◽  
2021 ◽  
Vol 10 (2) ◽  
pp. 100
Author(s):  
Hisham M. Almongy ◽  
Fatma Y. Alshenawy ◽  
Ehab M. Almetwally ◽  
Doaa A. Abdo
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Method ◽  
Likelihood Method ◽  
Estimation Methods ◽  
Type Ii ◽  
Type Ii Censoring ◽  
Progressive Type ◽  
Transformer Insulation ◽  
Censoring Scheme ◽  
Progressive Type Ii Censoring

In this paper, the Weibull extension distribution parameters are estimated under a progressive type-II censoring scheme with random removal. The parameters of the model are estimated using the maximum likelihood method, maximum product spacing, and Bayesian estimation methods. In classical estimation (maximum likelihood method and maximum product spacing), we did use the Newton–Raphson algorithm. The Bayesian estimation is done using the Metropolis–Hastings algorithm based on the square error loss function. The proposed estimation methods are compared using Monte Carlo simulations under a progressive type-II censoring scheme. An empirical study using a real data set of transformer insulation and a simulation study is performed to validate the introduced methods of inference. Based on the result of our study, it can be concluded that the Bayesian method outperforms the maximum likelihood and maximum product-spacing methods for estimating the Weibull extension parameters under a progressive type-II censoring scheme in both simulation and empirical studies.

scholarly journals New Regression Models Based on the Unit-Sinh-Normal Distribution: Properties, Inference, and Applications

Mathematics ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1231
Author(s):  
Guillermo Martínez-Flórez ◽  
Roger Tovar-Falón
Keyword(s):  
Maximum Likelihood ◽  
Regression Models ◽  
Maximum Likelihood Method ◽  
Real Data ◽  
Random Variable ◽  
Maximum Likelihood Estimates ◽  
Likelihood Method ◽  
Data Sets ◽  
Modeling Data ◽  
Positive Support

In this paper, two new distributions were introduced to model unimodal and/or bimodal data. The first distribution, which was obtained by applying a simple transformation to a unit-Birnbaum–Saunders random variable, is useful for modeling data with positive support, while the second is appropriate for fitting data on the (0,1) interval. Extensions to regression models were also studied in this work, and statistical inference was performed from a classical perspective by using the maximum likelihood method. A small simulation study is presented to evaluate the benefits of the maximum likelihood estimates of the parameters. Finally, two applications to real data sets are reported to illustrate the developed methodology.

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