The Bayesian estimation approach is a non-classical estimation technique in statistical inference and is very useful in real world situation. The aim of this paper is to study the Bayes estimators of the parameter of exponential distribution under different loss functions and compared among them as well as with the classical estimator named maximum likelihood estimator (MLE). Since exponential distribution is the lifetime distribution, we have studied exponential distribution using gamma prior. Here the gamma prior is used as the prior distribution of exponential distribution for finding the Bayes estimator. In our study we also used different symmetric and asymmetric loss functions such as squared error loss function, quadratic loss function, modified linear exponential (MLINEX) loss function and non-linear exponential (NLINEX) loss function. We have used simulated data using R-coding to find out the mean squared error (MSE) of different loss functions and hence found that non-classical estimator is better than classical estimator. Finally, mean square error (MSE) of the estimators of different loss functions are presented graphically.

The Bayesian estimation approach is a non-classical device in the estimation part of statistical inference which is very useful in real world situation. The main objective of this paper is to study the Bayes estimators of the parameter of Power function distribution. In Bayesian estimation loss function, prior distribution and posterior distribution are the most important ingredients. In real life we try to minimize the loss and want to know some prior information about the problem to solve it accurately. The well known conjugate priors are considered for finding the Bayes estimator. In our study we have used different symmetric and asymmetric loss functions such as squared error loss function, quadratic loss function, modified linear exponential (MLINEX) loss function and non-linear exponential (NLINEX) loss function. The performance of the obtained estimators for different types of loss functions are then compared among themselves as well as with the classical maximum likelihood estimator (MLE). Mean Square Error (MSE) of the estimators are also computed and presented in graphs.

Lorentz Transformations generally describe the transformations for observations between mechanical phenomenon systems in relative motion. We all know that the electrical charge of associate isolated system is relativistically invariant. We have studied the volume charge density in Special and Most General Lorentz Transformations. If one frame moves on x-axis then we will notice this in Special Lorentz Transformation. On the other hand if the motion of the moving frame is not on the x-axis relative to the rest frame however the motion is on any arbitrary direction then we will notice this formula for the Most General Lorentz Transformation. We also investigated the changes of the volume charge density of moving system in terms of that of rest system in Most General Lorentz Transformations at different angles and velocities.

The Lo rentz transformation is well known. In this paper, we have presented various types of applications of different Lorenz Transformat ions according to the nature of movement of one inertial frame relat ive to the other inertial frame such as relativistic aberration, relativ istic Doppler's effect and reflection of light ray by a moving mirro r. When one frame moves along X-axis with respect to the rest frame then we can find these applications for special Lo rentz transformation. When the motion o f the mov ing frame is not along X-axis relat ive to the rest frame but the mot ion is along any arbitrary direction then we can find these formulae for most general Lorentz transformation. We can generate these formulae fo r d ifferent types of most general Lorentz transformations using mixed number, quaternion and geometric product.

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