scholarly journals Studying the Third Cumulant of the Mixture of Dirichlet-multinomial Distributions

2021 ◽  
Vol 69 (2) ◽  
pp. 96-100
Author(s):  
Farzana Afroz
Keyword(s):  
Mean Squared Error ◽  
Multinomial Distribution ◽  
Finite Mixture ◽  
Multinomial Data ◽  
The Third ◽  
Squared Error ◽  
Lack Of Fit ◽  
Mathematical Expressions ◽  
Overdispersion Parameter ◽  
Deviance Statistic

Traditionally, the overdispersion parameter ϕ is estimated by using Pearson’s lack of fit statistic X2or the Deviance statistic D, which do not perform well in the case of sparse data. This paper particularly focuses on an estimator ϕnew of overdispersion parameter which was proposed for sparse multinomial data. The estimator was derived on the basis of an assumption on the 3rd cumulant of the response variable.When the data comes from the Dirichlet-multinomial distribution ϕnew is known to have the lowest root mean squared error comparing to the other three estimators. In this paper the 1st to 3rd order raw moments of the finite mixture of Dirichlet-multinomial distributions are derived, which results in complicated mathematical expressions. Furthermore, it is found that the 3rd cumulant of this mixture does not satisfy the assumption which is considered in the derivation of ϕnew . Dhaka Univ. J. Sci. 69(2): 96-100, 2021 (July)

scholarly journals Comparison Between Two Multinomial Overdispersion Models Through Simulation

2020 ◽  
Vol 68 (1) ◽  
pp. 45-48
Author(s):  
Farzana Afroz ◽  
Zillur Rahman Shabuz
Keyword(s):  
Mixture Model ◽  
Simulation Study ◽  
Multinomial Distribution ◽  
Finite Mixture Model ◽  
Finite Mixture ◽  
Multinomial Model ◽  
Pollen Data ◽  
Multinomial Data ◽  
The Difference ◽  
Overdispersion Parameter

A key assumption when using the multinomial distribution is that the observations are independent. In many practical situations, the observations could be correlated or clustered and the probabilities within each cluster might vary, which may lead to overdispersion. In this paper we discuss two well-known approaches to model overdispersed multinomial data, the Dirichlet-multinomial model and the finite-mixture model. The difference between these two models has been illustrated via simulation study. The forest pollen data is considered as a practical example of overdisperse multinomial data. The overdispersion parameter,φ, has been estimated using two classical estimators. Dhaka Univ. J. Sci. 68(1): 45-48, 2020 (January)

scholarly journals Multicomponent Inverse Lomax Stress-Strength Reliability

2020 ◽  
pp. 72-80
Author(s):  
Nada S. Karam ◽  
Shahbaa M. Yousif ◽  
Bushra J. Tawfeeq
Keyword(s):  
Maximum Likelihood ◽  
Mean Squared Error ◽  
Scale Parameter ◽  
Model Systems ◽  
Estimation Methods ◽  
Squared Error ◽  
Mathematical Expressions ◽  
Distribution Parameters ◽  
The Mean ◽  
Inverse Lomax Distribution

In this article we derive two reliability mathematical expressions of two kinds of s-out of -k stress-strength model systems; and . Both stress and strength are assumed to have an Inverse Lomax distribution with unknown shape parameters and a common known scale parameter. The increase and decrease in the real values of the two reliabilities are studied according to the increase and decrease in the distribution parameters. Two estimation methods are used to estimate the distribution parameters and the reliabilities, which are Maximum Likelihood and Regression. A comparison is made between the estimators based on a simulation study by the mean squared error criteria, which revealed that the maximum likelihood estimator works the best.

Use of reflectance spectroscopy to estimate the organic carbon and CaCO3 contents of soils

2012 ◽  
Vol 61 (2) ◽  
pp. 277-290 ◽  
Author(s):  
Ádám Csorba ◽  
Vince Láng ◽  
László Fenyvesi ◽  
Erika Michéli
Keyword(s):  
Organic Carbon ◽  
Least Squares ◽  
Partial Least Squares ◽  
Partial Least Squares Regression ◽  
Mean Squared Error ◽  
Reflectance Spectroscopy ◽  
Least Squares Regression ◽  
Root Mean Squared Error ◽  
Squared Error

Napjainkban egyre nagyobb igény mutatkozik olyan technológiák és módszerek kidolgozására és alkalmazására, melyek lehetővé teszik a gyors, költséghatékony és környezetbarát talajadat-felvételezést és kiértékelést. Ezeknek az igényeknek felel meg a reflektancia spektroszkópia, mely az elektromágneses spektrum látható (VIS) és közeli infravörös (NIR) tartományában (350–2500 nm) végzett reflektancia-mérésekre épül. Figyelembe véve, hogy a talajokról felvett reflektancia spektrum információban nagyon gazdag, és a vizsgált tartományban számos talajalkotó rendelkezik karakterisztikus spektrális „ujjlenyomattal”, egyetlen görbéből lehetővé válik nagyszámú, kulcsfontosságú talajparaméter egyidejű meghatározása. Dolgozatunkban, a reflektancia spektroszkópia alapjaira helyezett, a talajok ösz-szetételének meghatározását célzó módszertani fejlesztés első lépéseit mutatjuk be. Munkánk során talajok szervesszén- és CaCO3-tartalmának megbecslését lehetővé tévő többváltozós matematikai-statisztikai módszerekre (részleges legkisebb négyzetek módszere, partial least squares regression – PLSR) épülő prediktív modellek létrehozását és tesztelését végeztük el. A létrehozott modellek tesztelése során megállapítottuk, hogy az eljárás mindkét talajparaméter esetében magas R2értéket [R2(szerves szén) = 0,815; R2(CaCO3) = 0,907] adott. A becslés pontosságát jelző közepes négyzetes eltérés (root mean squared error – RMSE) érték mindkét paraméter esetében közepesnek mondható [RMSE (szerves szén) = 0,467; RMSE (CaCO3) = 3,508], mely a reflektancia mérési előírások standardizálásával jelentősen javítható. Vizsgálataink alapján arra a következtetésre jutottunk, hogy a reflektancia spektroszkópia és a többváltozós kemometriai eljárások együttes alkalmazásával, gyors és költséghatékony adatfelvételezési és -értékelési módszerhez juthatunk.

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.

Image Quality Enhancing by Efficient Histogram Equalization

2014 ◽  
Vol 2 (2) ◽  
pp. 47-58
Author(s):  
Ismail Sh. Baqer
Keyword(s):  
Image Quality ◽  
Contrast Enhancement ◽  
Mean Squared Error ◽  
Signal To Noise Ratio ◽  
Histogram Equalization ◽  
Gray Level ◽  
Signal To Noise ◽  
Squared Error ◽  
Noise Ratio

A two Level Image Quality enhancement is proposed in this paper. In the first level, Dualistic Sub-Image Histogram Equalization DSIHE method decomposes the original image into two sub-images based on median of original images. The second level deals with spikes shaped noise that may appear in the image after processing. We presents three methods of image enhancement GHE, LHE and proposed DSIHE that improve the visual quality of images. A comparative calculations is being carried out on above mentioned techniques to examine objective and subjective image quality parameters e.g. Peak Signal-to-Noise Ratio PSNR values, entropy H and mean squared error MSE to measure the quality of gray scale enhanced images. For handling gray-level images, convenient Histogram Equalization methods e.g. GHE and LHE tend to change the mean brightness of an image to middle level of the gray-level range limiting their appropriateness for contrast enhancement in consumer electronics such as TV monitors. The DSIHE methods seem to overcome this disadvantage as they tend to preserve both, the brightness and contrast enhancement. Experimental results show that the proposed technique gives better results in terms of Discrete Entropy, Signal to Noise ratio and Mean Squared Error values than the Global and Local histogram-based equalization methods

scholarly journals Thematic Maps for the Variation of Bearing Capacity of Soil Using SPTs and MATLAB

Geosciences ◽  
2020 ◽  
Vol 10 (9) ◽  
pp. 329
Author(s):  
Mahdi O. Karkush ◽  
Mahmood D. Ahmed ◽  
Ammar Abdul-Hassan Sheikha ◽  
Ayad Al-Rumaithi
Keyword(s):  
Bearing Capacity ◽  
Mean Squared Error ◽  
Ground Level ◽  
The Other ◽  
Thematic Maps ◽  
First Order ◽  
Squared Error ◽  
Order Polynomial ◽  
Interpolation Polynomials ◽  
Penetration Tests

The current study involves placing 135 boreholes drilled to a depth of 10 m below the existing ground level. Three standard penetration tests (SPT) are performed at depths of 1.5, 6, and 9.5 m for each borehole. To produce thematic maps with coordinates and depths for the bearing capacity variation of the soil, a numerical analysis was conducted using MATLAB software. Despite several-order interpolation polynomials being used to estimate the bearing capacity of soil, the first-order polynomial was the best among the other trials due to its simplicity and fast calculations. Additionally, the root mean squared error (RMSE) was almost the same for the all of the tried models. The results of the study can be summarized by the production of thematic maps showing the variation of the bearing capacity of the soil over the whole area of Al-Basrah city correlated with several depths. The bearing capacity of soil obtained from the suggested first-order polynomial matches well with those calculated from the results of SPTs with a deviation of ±30% at a 95% confidence interval.

scholarly journals Industrial Control under Non-Ideal Measurements: Data-Based Signal Processing as an Alternative to Controller Retuning

Sensors ◽  
2021 ◽  
Vol 21 (4) ◽  
pp. 1237
Author(s):  
Ivan Pisa ◽  
Antoni Morell ◽  
Ramón Vilanova ◽  
Jose Lopez Vicario
Keyword(s):  
Mean Squared Error ◽  
Control Strategies ◽  
Treatment Plant ◽  
Industrial Control ◽  
Output Data ◽  
Complex Processes ◽  
Squared Error ◽  
Complex Design ◽  
Solution Design ◽  
Delay Correction

Industrial environments are characterised by the non-lineal and highly complex processes they perform. Different control strategies are considered to assure that these processes are correctly performed. Nevertheless, these strategies are sensible to noise-corrupted and delayed measurements. For that reason, denoising techniques and delay correction methodologies should be considered but, most of these techniques require a complex design and optimisation process as a function of the scenario where they are applied. To alleviate this, a complete data-based approach devoted to denoising and correcting the delay of measurements is proposed here with a two-fold objective: simplify the solution design process and achieve its decoupling from the considered control strategy as well as from the scenario. Here it corresponds to a Wastewater Treatment Plant (WWTP). However, the proposed solution can be adopted at any industrial environment since neither an optimization nor a design focused on the scenario is required, only pairs of input and output data. Results show that a minimum Root Mean Squared Error (RMSE) improvement of a 63.87% is achieved when the new proposed data-based denoising approach is considered. In addition, the whole system performance show that similar and even better results are obtained when compared to scenario-optimised methodologies.

scholarly journals A Novel Computational Intelligence Approach for Coal Consumption Forecasting in Iran

2021 ◽  
Vol 13 (14) ◽  
pp. 7612
Author(s):  
Mahdis sadat Jalaee ◽  
Alireza Shakibaei ◽  
Amin GhasemiNejad ◽  
Sayyed Abdolmajid Jalaee ◽  
Reza Derakhshani
Keyword(s):  
Hybrid Method ◽  
Computational Intelligence ◽  
Energy Demand ◽  
Mean Squared Error ◽  
Absolute Error ◽  
Coal Consumption ◽  
Squared Error ◽  
Artificial Neural ◽  
Socio Economic Variables ◽  
Intelligence Approach

Coal as a fossil and non-renewable fuel is one of the most valuable energy minerals in the world with the largest volume reserves. Artificial neural networks (ANN), despite being one of the highest breakthroughs in the field of computational intelligence, has some significant disadvantages, such as slow training, susceptibility to falling into a local optimal points, sensitivity of initial weights, and bias. To overcome these shortcomings, this study presents an improved ANN structure, that is optimized by a proposed hybrid method. The aim of this study is to propose a novel hybrid method for predicting coal consumption in Iran based on socio-economic variables using the bat and grey wolf optimization algorithm with an artificial neural network (BGWAN). For this purpose, data from 1981 to 2019 have been used for modelling and testing the method. The available data are partly used to find the optimal or near-optimal values of the weighting parameters (1980–2014) and partly to test the model (2015–2019). The performance of the BGWAN is evaluated by mean squared error (MSE), mean absolute error (MAE), root mean squared error (RMSE), standard deviation error (STD), and correlation coefficient (R^2) between the output of the method and the actual dataset. The result of this study showed that BGWAN performance was excellent and proved its efficiency as a useful and reliable tool for monitoring coal consumption or energy demand in Iran.

scholarly journals Complete subset averaging with many instruments

2020 ◽  
Author(s):  
Seojeong Lee ◽  
Youngki Shin
Keyword(s):  
Demand Function ◽  
Simulation Experiment ◽  
Mean Squared Error ◽  
Asymptotic Optimality ◽  
Weighted Average ◽  
Subset Size ◽  
Extensive Simulation ◽  
Squared Error ◽  
Many Instruments ◽  
Class Of Estimators

Summary We propose a two-stage least squares (2SLS) estimator whose first stage is the equal-weighted average over a complete subset with k instruments among K available, which we call the complete subset averaging (CSA) 2SLS. The approximate mean squared error (MSE) is derived as a function of the subset size k by the Nagar (1959) expansion. The subset size is chosen by minimising the sample counterpart of the approximate MSE. We show that this method achieves asymptotic optimality among the class of estimators with different subset sizes. To deal with averaging over a growing set of irrelevant instruments, we generalise the approximate MSE to find that the optimal k is larger than otherwise. An extensive simulation experiment shows that the CSA-2SLS estimator outperforms the alternative estimators when instruments are correlated. As an empirical illustration, we estimate the logistic demand function in Berry et al. (1995) and find that the CSA-2SLS estimate is better supported by economic theory than are the alternative estimates.

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