A multiple dependent state (MDS) sampling plan is developed based on the coefficient of variation of the quality characteristic which follows a normal distribution with unknown mean and variance. The optimal plan parameters of the proposed plan are solved by a nonlinear optimization model, which satisfies the given producer's risk and consumer's risk at the same time and minimizes the sample si...

The relationship between textural properties of selected Nigeria rocks and penetration rate of top-hole hammer drill was investigated. These rock samples were tested in the laboratory for mineral composition, silica content and porosity. Also, average grain size and packing density were determined from photomicrograph of the samples using empirical equations proposed by researchers. Penetration...

We study bias arising as a result of nonlinear transformations of random variables in random or mixed effects models and its effect on inference in group-level studies or in meta-analysis. The findings are illustrated on the example of overdispersed binomial distributions, where we demonstrate considerable biases arising from standard log-odds and arcsine transformations of the estimated probab...

In this paper we study the network structure in music and attempt to compose music artificially. Networks are constructed with nodes and edges corresponding to musical notes and their co-occurrences. We analyze sample compositions from Bach, Mozart, Chopin, as well as other types of music including Chinese pop music. We observe remarkably similar properties in all networks constructed from the ...

The present study aimed at the development of the water deficit coefficient as a function of the Christiansen uniformity coefficient and relationship between the applied water depth and that required by a given crop, taking into account that the water distribution by the sprinkler follows a normal distribution. Another objective was to compare the experimental results to those obtained through ...

We rewrite Arthur’s asymptotic formula for weighted orbital integrals on real groups with the aid of a residue calculus and extend the resulting formula to the Schwartz space. Then we extract the available information about the coefficients in the decomposition of the Fourier transforms of Arthur’s invariant distributions IM (γ) in terms of standard solutions of the pertinent holonomic system o...

The Stieltjes coefficients γk(a) arise in the expansion of the Hurwitz zeta function ζ(s, a) about its single simple pole at s = 1 and are of fundamental and long-standing importance in analytic number theory and other disciplines. We present an array of exact results for the Stieltjes coefficients, including series representations and summatory relations. Other integral representations provide...

In this paper we propose a block shrinkage method in the wavelet domain for estimating an unknown function in the presence of Gaussian noise. This shrinkage utilizes an empirical Bayes, block-adaptive approach that accounts for the sparseness of the representation of the unknown function. The modeling is accomplished by using a mixture of two normal-inverse gamma distributions as a joint prior ...

This work is motivated by a meta-analysis case study on antipsychotic medications. The Michaelis-Menten curve is employed to model the nonlinear relationship between the dose and D2 receptor occupancy across multiple studies. An intraclass correlation coefficient (ICC) is used to quantify the heterogeneity across studies. To interpret the size of heterogeneity, an accurate estimate of ICC and i...