Seiichi Yasui, Yoshikazu Ojima
A SYNTHESIZED ESTIMATOR IN UNBALANCED NESTED DESIGNS WITH TWO STAGES

Nested designs are one of experimental designs to evaluate and/or determine precision of measurement results, statistically. Unbalanced designs have interesting statistical problems, one of which is that an unbiased estimator of variance components is not unique. In our study, a new estimator of a variance component for the top stage of two-stages unbalanced nested designs is proposed. The performance of our estimator outperforms conventional estimators from the aspect of estimation accuracy.

Viktor Witkovský
NUMERICAL INVERSION OF A CHARACTERISTIC FUNCTION: AN ALTERNATIVE TOOL TO FORM THE PROBABILITY DISTRIBUTION OF OUTPUT QUANTITY IN LINEAR MEASUREMENT MODELS

The exact (statistical) inference frequently require evaluation of the probability density function (PDF), the cumulative distribution function (CDF), and/or the quantile function (QF) of a random variable from its (known) characteristic function (CF), which is defined as a Fourier transform of its probability distribution function. Working with CFs provides an alternative (frequently more simple) route, than working directly with PDFs and/or CDFs. In particular, derivation of the CF of a weighted sum of independent random variable is a very simple and trivial task (given the CFs of the random variables). However, the analytical derivation of the PDF and/or CDF by using the Fourier transform is available only in special cases. Thus, in most practical situation, a numerical derivation of the PDF/CDF from the CF is an indispensable tool. In metrological applications, such approach can be used to form the probability distribution for the output quantity of a measurement model of additive, linear or generalized linear form. In this paper we shall present a brief overview of some efficient approaches for numerical inversion of the characteristic function, which are especially suitable for typical metrological applications. The suggested numerical approaches are based on the Gil-Pelaez inverse formula and on the approximation by discrete Fourier transform (DFT) and the FFT algorithm for computing PDF/CDF of (univariate) continuous random variables. We also present a sketch of the MATLAB implementation, together with several examples to illustrate its applicability.

Serhii W. Zabolotnii, Zygmunt Lech Warsza
SEMI-PARAMETRIC POLYNOMIAL MODIFICATION OF CUSUM ALGORITHMS FOR CHANGE-POINT DETECTION OF NON-GAUSSIAN SEQUENCES

Expansion of logarithm likelihood ratio in the stochastic series is used to find the sequential change-point detection of non-Gaussian sequences. The moment criteria of the minimum of upper limit error probabilities sum is used to find the expansion coefficients. The proposed method is a semi-parametric type of CUSUM (cumulative sum) algorithm which needs of higher-order statistics. The experimental results show that polynomial algorithms are more effective in comparison with similar non-parametric procedures.

Adriana Vâlcu
COMPARISON BETWEEN THE NATIONAL PROTOTYPE OF THE KILOGRAM AND STAINLESS STEEL MASS STANDARDS

In 2013, the National Prototype of the Kilogram (NPK) No.2 belonging to Romania, together with stainless steel kilogram standard Ni81, received an updated mass value from BIPM. Therefore, the first task after their receiving from BIPM was to perform comparisons between NPK and reference kilograms stainless steel standards. In the paper are described mass standards, weighing scheme used for comparisons, calculations of mass and associated uncertainties, as the mass change for all weights involved. It is also presented a comparison between Romanian CMC(s) and other countries for this important stage of dissemination of mass unit.

Tomomichi Suzuki, Akimasa Katakura, Rei Miyazawa, Natsuki Sano
PRECISION EVALUATION FOR NON-QUANTITATIVE MEASUREMENTS ~ BINARY AND ORDINAL CATEGORICAL CASES ~

Precision evaluation in quantitative measurements is a thoroughly discussed topic and the established methods are in use. Many methods are proposed for qualitative data, but their effectiveness and statistical properties are not so clear. This paper examines their properties by applying some of the major methods and then by comparing the applied results. The comparisons are made to binary data and also to ordinal categorical data. Some of the similarities and the differences among the methods became clear after examining the results.