In this paper, we have derived Bayesian estimation for the parameters and reliability function of Perks distribution based on two different loss functions, Lindley’s approximation has been used to obtain those values. It is assumed that the parameter behaves as a random variable have a Gumbell Type P prior with non-informative is used. And after the derivation of mathematical formulas of those estimations, the simulation method was used for comparison depending on mean square error (MSE) values and integrated mean absolute percentage error (IMAPE) values respectively. Among of conclusion that have been reached, it is observed that, the LE-NR estimate introduced the best perform for estimating the parameter λ.

In the current study, the researchers have been obtained Bayes estimators for the shape and scale parameters of Gamma distribution under the precautionary loss function, assuming the priors, represented by Gamma and Exponential priors for the shape and scale parameters respectively. Moment, Maximum likelihood estimators and Lindley’s approximation have been used effectively in Bayesian estimation.

Based on Monte Carlo simulation method, those estimators are compared depending on the mean squared errors (MSE’s). The results show that, the performance of Bayes estimator under precautionary loss function with Gamma and Exponential priors is better than other estimates in all cases.

This paper deals with the blow-up properties of positive solutions to a parabolic system of two heat equations, defined on a ball in  associated with coupled Neumann boundary conditions of exponential type. The upper bounds of blow-up rate estimates are derived. Moreover, it is proved that the blow-up in this problem can only occur on the boundary.

The Log-Logistic distribution is one of the important statistical distributions as it can be applied in many fields and biological experiments and other experiments, and its importance comes from the importance of determining the survival function of those experiments. The research will be summarized in making a comparison between the method of maximum likelihood and the method of least squares and the method of weighted least squares to estimate the parameters and survival function of the log-logistic distribution using the comparison criteria MSE, MAPE, IMSE, and this research was applied to real data for breast cancer patients. The results showed that the method of Maximum likelihood best in the case of estimating the paramete

In this paper, Bayes estimators for the shape and scale parameters of Weibull distribution have been obtained using the generalized weighted loss function, based on Exponential priors. Lindley’s approximation has been used effectively in Bayesian estimation. Based on theMonte Carlo simulation method, those estimators are compared depending on the mean squared errors (MSE’s).

In many applications such as production, planning, the decision maker is important in optimizing an objective function that has fuzzy ratio two functions which can be handed using fuzzy fractional programming problem technique. A special class of optimization technique named fuzzy fractional programming problem is considered in this work when the coefficients of objective function are fuzzy. New ranking function is proposed and used to convert the data of the fuzzy fractional programming problem from fuzzy number to crisp number so that the shortcoming when treating the original fuzzy problem can be avoided. Here a novel ranking function approach of ordinary fuzzy numbers is adopted for ranking of triangular fuzzy numbers with simpler an

     In this paper, some estimators for the unknown shape parameter and reliability function of Basic Gompertz distribution have been obtained, such as Maximum likelihood estimator and Bayesian estimators under Precautionary loss function using Gamma prior and Jefferys prior. Monte-Carlo simulation is conducted to compare mean squared errors (MSE) for all these estimators for the shape parameter and integrated mean squared error (IMSE's) for comparing the performance of the Reliability estimators. Finally, the discussion is provided to illustrate the results that summarized in tables.

     In this work,   polynomials  and the finite q-exponential operator  are constructed. The operator  is used to combine an operator proof of the generating function with its extension, Mehler's formula with its extension and Roger's formula for the polynomials . The generating function with its extension,  Mehler's formula with its extension and Rogers formula for Al-Salam-Carlitz polynomials  are deduced by giving special values to polynomials .

The present paper analyzes the signal emitting from the Reticle during changing the spot size of laser falling on the disk and shows the optimum frequency and the amount of energy window in different patterns of modulator (Reticle).  All results are obtained by establishing   a special program named “Disk optical modulator version 3" using the language visual basic 6 ahich contains many parameters. All models of optical modulator consist of twenty sectors, ten sectors are opaque and other ten sectors are transmitted for the laser. The number of sectors depends on several factors as chopping frequency, power transparent and modulation transfer function.   It has been demonstrated by simulations, the optimal

Solar energy is one of the immeasurable renewable energy in power generation for a green, clean and healthier environment. The silicon-layer solar panels absorb sun energy and converts it into electricity by off-grid inverter. Electricity is transferred either from this inverter or from transformer, consumed by consumption unit(s) available for residential or economic purposes. The artificial neural network is the foundation of artificial intelligence and solves many complex problems which are difficult by statistical methods or by humans. In view of this, the purpose of this work is to assess the performance of the Solar - Transformer - Consumption (STC) system. The system may be in complete breakdown situation due to failure of both so