Gumbel distribution was dealt with great care by researchers and statisticians. There are traditional methods to estimate two parameters of Gumbel distribution known as Maximum Likelihood, the Method of Moments and recently the method of re-sampling called (Jackknife). However, these methods suffer from some mathematical difficulties in solving them analytically. Accordingly, there are other non-traditional methods, like the principle of the nearest neighbors, used in computer science especially, artificial intelligence algorithms, including the genetic algorithm, the artificial neural network algorithm, and others that may to be classified as meta-heuristic methods. Moreover, this principle of nearest neighbors has useful statistical features. The objective of this paper is thus to propose a new algorithm where it allows getting the estimation of the parameters of Gumbel probability distribution directly. Furthermore, it overcomes the mathematical difficulties in this matter without need to the derivative of the likelihood function. Taking simulation approach under consideration as empirical experiments where a hybrid method performs optimization of these three traditional methods. In this regard, comparisons have been done between the new proposed method and each pair of the traditional methods mentioned above by efficiency criterion Root of Mean Squared Error (RMSE). As a result, (36) experiments of different combinations of initial values of two parameters (λ: shift parameter and θ: scale parameter) in three values that take four different sample sizes for each experiment. To conclude, the proposed algorithm showed its superiority in all simulation combinations associated with all sample sizes for the two parameters (λ and θ). In addition, the method of Moments was the best in estimating the shift parameter (λ) and the method of Maximum Likelihood was in estimating the scale parameter (θ).
Simple and sensitive spectrophotometric method is described based on the coupling reaction of tetracycline hydrochloride (TC. HCl) with diazotized 4-aminopyridine in bulk and pharmaceutical forms. Colored azo dye formed during this reaction is measured at 433 nm as a function of time. Factors affecting the reaction yield were studied and the conditions were optimized. The kinetic study involves initial rate and fixed time (10 minutes) procedures for constructing the calibration graphs to determine the concentration of (TC. HCl). The graphs were linear for both methods in concentration range of 10.0 to 100.0 μg.mL-1. The recommended procedure was applied successfully in the determination of (TC. HCl) in its commercial formulations.
Simple and sensitive spectrophotometric method is described based on the coupling reaction of tetracycline hydrochloride(TC. HCl) with diazotized 4-aminopyridine in bulk and pharmaceutical forms. Colored azo dye formed during this reaction is measured at 433 nm as a function of time. Factors affecting the reaction yield were studied and the conditions were optimized. The kinetic study involves initial rate and fixed time (10 minutes) procedures for constructing the calibration graphs to determine the concentration of (TC. HCl). The graphs were linear for both methods in concentration range of 10.0 to 100.0 µg.mL-1. The recommended procedure was applied successfully in the determination of (TC. HCl) in itscommercial formulations.
... Show MoreBy driven the moment estimator of ARMA (1, 1) and by using the simulation some important notice are founded, From the more notice conclusions that the relation between the sign and moment estimator for ARMA (1, 1) model that is: when the sign is positive means the root gives invertible model and when the sign is negative means the root gives invertible model. An alternative method has been suggested for ARMA (0, 1) model can be suitable when
Semi-parametric regression models have been studied in a variety of applications and scientific fields due to their high flexibility in dealing with data that has problems, as they are characterized by the ease of interpretation of the parameter part while retaining the flexibility of the non-parametric part. The response variable or explanatory variables can have outliers, and the OLS approach have the sensitivity to outliers. To address this issue, robust (resistance) methods were used, which are less sensitive in the presence of outlier values in the data. This study aims to estimate the partial regression model using the robust estimation method with the wavel
... Show MoreBaker's Yeast is an important additive among the substances, which improves bred quality, thus, a consideration has been made to study the conditions and parameters that affecting the production of the yeast in a batch fermenter experimentally and theoretically. Experimental runs were implemented in a 12-liter pilot-scale fermenter to predict the rate of growth and other parameters such as amount of additive consumed and the amount of heat generated. The process is modeled and performed using a computer programming prepped for this purpose, the model gave a good agreement comparing to the experimental work specially in the log phase.
The problem of frequency estimation of a single sinusoid observed in colored noise is addressed. Our estimator is based on the operation of the sinusoidal digital phase-locked loop (SDPLL) which carries the frequency information in its phase error after the noisy sinusoid has been acquired by the SDPLL. We show by computer simulations that this frequency estimator beats the Cramer-Rao bound (CRB) on the frequency error variance for moderate and high SNRs when the colored noise has a general low-pass filtered (LPF) characteristic, thereby outperforming, in terms of frequency error variance, several existing techniques some of which are, in addition, computationally demanding. Moreover, the present approach generalizes on existing work tha
... Show MoreIn this research we assumed that the number of emissions by time (𝑡) of radiation particles is distributed poisson distribution with parameter (𝑡), where < 0 is the intensity of radiation. We conclude that the time of the first emission is distributed exponentially with parameter 𝜃, while the time of the k-th emission (𝑘 = 2,3,4, … . . ) is gamma distributed with parameters (𝑘, 𝜃), we used a real data to show that the Bayes estimator 𝜃 ∗ for 𝜃 is more efficient than 𝜃̂, the maximum likelihood estimator for 𝜃 by using the derived variances of both estimators as a statistical indicator for efficiency
There many methods for estimation of permeability. In this Paper, permeability has been estimated by two methods. The conventional and modified methods are used to calculate flow zone indicator (FZI). The hydraulic flow unit (HU) was identified by FZI technique. This technique is effective in predicting the permeability in un-cored intervals/wells. HU is related with FZI and rock quality index (RQI). All available cores from 7 wells (Su -4, Su -5, Su -7, Su -8, Su -9, Su -12, and Su -14) were used to be database for HU classification. The plot of probability cumulative of FZI is used. The plot of core-derived probability FZI for both modified and conventional method which indicates 4 Hu (A, B, C and D) for Nahr Umr forma
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