Abstract The strength of a Ni-base superalloy depends strongly on its microstructure consisting cuboidal $${\gamma }^{^{\prime}}$$ γ ′ precipitates surrounded by narrow channels $$\gamma $$ matrix. According to the theory Orowan, movi...

The unmixed gamma distribution has been used extensively in fitting precipitation data. After the author [l] proposed a mixed distribution for precipitation series where zeros occur this distribution also began to be widely employed. Since it is often necessary to add precipitation, i.e. June plus July, for example, it is a great convenience to be able to accomplish this analytically and so avo...

The theoretical study of serum prolactin response to TRH during antithyroid treatment in hyperthyroid patients was determined. Formulae of fuzzy gamma distributions, fuzzy reliability functions and its  -cut sets are presented. Using a Fuzzy reliability analysis based on gamma distribution, we showed that changes from normal serum levels of T3 and T4 are associated with changes in prolactin re...

We derive distributions of ratio for two independent gamma variables and two independent inverted gamma variables and then we observe the skewness of two ratio densities. We then consider inference on reliability in two independent gamma random variables and two independent inverted gamma random variables each having known shape parameters.

* Correspondence: [email protected] Department of Medical Education, Faculty of Medicine, 06490, Bahçelievler, Ankara, Turkey Full list of author information is available at the end of the article Abstract In this article, a method is developed to transform the chance-constrained programming problem into a deterministic problem. We have considered a chance-constrained programming problem u...

Semicontinuous data consist of a combination of a point-mass at zero and a positive skewed distribution. This type of non-negative data distribution is found in data from many fields, but presents unique challenges for analysis. Specifically, these data cannot be analyzed using positive distributions, but distributions that are unbounded are also likely a poor fit. Two-part models incorporate b...

Abstract We discuss estimating the probability that sum of nonnegative independent and identically distributed random variables falls below a given threshold, i.e., $$\mathbb {P}(\sum _{i=1}^{N}{X_i} \le \gamma )$$ P ( ∑ i = <mml...

Abstract As discussed in the first chapter, main objective of our work is to generalize Krull-Webster’s theory multiple $$\log \Gamma $$ log Γ -type functions and explore properties these that are analogues classical gamma function.

In this paper we extend autoregressive models to fit time series that have three layers of seasonality, i.e. triple seasonal (TSAR) models, and introduce the Bayesian inference for these TSAR models. Assuming model errors are normally distributed employing priors, Jeffreys', g, normal-gamma on parameters, derive marginal posterior distributions parameters. particular, show be multivariate t gam...