When studying probability theory, the moment generating function (MGF) always appears when discussing statistics that indicate the characteristics of a probability distribution, such as expectation, ...

"Multiplying polynomials allows you to count combinations"—this is a series where you can experience this mysterious tool from scratch. This is the final installment of the 6-part series. This time, ...

ABSTRACT: We obtain a closed form expression for the joint probability mass function of the occupation times for a Three-State Markov chain. Our representation extends the long-standing result for a ...

As is well known, the normal distribution is a key tool in probability and statistics. It can be described as a distribution that obeys a universal rule derived from one of the most important theorems ...

What Is A Probability Density Function? A probability density function, also known as a bell curve, is a fundamental statistics concept, that describes the likelihood of a continuous random variable ...

We propose a method of constructing analytical, closed-form expressions for electrostatic/Newtonian potentials of non-uniform polyhedral bodies, in which the density distributions are polynomials of ...

Abstract: For structural performance functions with characteristics of multivariable, non-normality, small failure probability and nonlinearity, it is usually difficult to pursue satisfactory accuracy ...

When making economic decisions, humans can evaluate probabilities and magnitudes of outcomes in an idiosyncratic way that can lead to poor decisions. This suggests that the internal functions that map ...

Energy is at the heart of the climate challenge – and key to the solution. Generating electricity and heat by burning fossil fuels – coal, oil, or gas – causes a large chunk of the greenhouse gases, ...

Generalized method of moments based on probability generating function is considered. Estimation and model testing are unified using this approach which also leads to distribution free chi-square ...