Abstract. Consider the random normal matrix ensemble associated with a potential on the plane which is sufficiently strong near infinity. It is known that, to a first approximation, the eigenvalues obey a certain equilibrium distribution, given by Frostman’s solution to the minimum energy problem of weighted logarithmic potential theory. On a finer scale, one can consider fluctuations of eigenv...

In statistic tests, the probability distribution of the statistics is important. When samples are drawn from population N (µ, σ(2)) with a sample size of n, the distribution of the sample mean X̄ should be a normal distribution N (µ, σ(2)/n). Under the null hypothesis µ = µ0, the distribution of statistics [Formula: see text] should be standardized as a normal distribution. When the variance of ...

All biological samples emit ultra-low intensity light without any external stimulation. Recently, scientific communities have paid particular attention to this phenomenon, known as ultra-weak photon emission (UPE). UPE has been introduced in the literature as an alternative for biophoton, low-level chemiluminescence and ultra-weak bioluminescence, while it differs from ordinary bioluminescence,...

The Weibull distribution is widely employed in several areas of engineering because it is an extremely flexible distribution with different shapes. Moreover, it can include characteristics of several other distributions. However, successful usage of Weibull distribution depends on estimation accuracy for three parameters of scale, shape and location. This issue shifts the attentions to the requ...

Tolerancing is one of the most important tools for planning, controlling, and improving quality in the industry. Tolerancing conducted by design engineers to meet customers’ needs is a prerequisite for producing high-quality products. Engineers use handbooks to conduct tolerancing. While use of statistical methods for tolerancing is not a new concept, engineers often use known distributions, in...