Design of SkSP-R Plan for Popular Statistical Distributions

The design of a Skip-lot sampling plan of type SkSP-R is presented for time truncated life test for the Weibull, Exponentiated Weibull, and Birnbaum-Saunders lifetime distributions. The plan parameters of the SkSP-R plan under these three distributions are determined through a nonlinear optimization problem. Tables are also constructed for each distribution. The advantages of the proposed plan over the existing sampling schemes are discussed. Application of the proposed plan is explained with the help of an example. The Birnbaum-Saunders distribution is economically superior to other two distributions in terms of minimum average sample number.

Специфика статистики упругих и деформационно-прочностных свойств высокопрочных волокон полипропилена

Regularities of statistical distributions of a complex of mechanical properties, including the module of elasticity (E), strength () and strain at break (b), high-strength industrial oriented polypropylene (PP) fibers have been analyzed using the Weibull and Gauss models based on large a wide array of measurements (50 identical samples in each series). The values of the statistical Weibull modulus (m) - a parameter characterizing the scatter of the measured values of the data arrays of E,  and b – have been estimated for the PP samples of two types: single fibers (monofilaments) and multifilament fibers consisting from several hundred single fibers. For the PP multifilament fibers, a more correct description of the distributions of E,  and b has been received both in the framework of the normal distribution (Gaussian distribution) and in the framework of the Weibull distribution in comparison with the description of such distributions for the PP monofilaments. The influence of the polymer chain conformation on the regularities of the statistical distributions of E,  and b for the high-strength oriented polymeric materials with different chemical chain structures and the correctness of their descriptions in the framework of the Gauss and Weibull models have been analyzed. For this purpose, the values of m calculated in this work for PP with a helical chain conformation have been compared with the values of m determined by us earlier for ultra-high molecular weight polyethylene and polyamide-6 with the chain conformations in the form of an in-plane trans-zigzag.

Correlation of Statistical Distributions of the Dimension of Yeast Cells Attached to the Substrate and Its Surface Electrical Potential

The ability of cells to adhere to substrates is an important factor for the effectiveness of biotechnologies and bioimplants. This research demonstrates that the statistical distribution of the sizes of the cells (Saccharomyces cerevisiae) attached to the substrate surface correlates with the statistical distribution of electrical potential on the substrate’s surface. Hypothetically, this behavior should be taken into consideration during the processing of surfaces when cell adhesion based on cell size is required.

Development of a method for differential analysis of data on the arterial blood oxygenation in healthy adults

Monitoring of arterial blood saturation with oxygen (oxygenation) has gained special significance as a result of the COVID-19 pandemic. A new method for computer processing of saturation records (so-called SaO2 signals), based on the study of differentials (increments) from signals, was proposed. Finding a differential for a time series involves calculating the difference between the pairs of its adjacent elements. The differential is non-zero only if the elements in a pair are different. The study of differentials together with primary signals for a set of records (20 subjects) shows that the spectrum of observed levels of blood saturation is discrete and limited (from 2 to 10 levels). In addition, changes in saturation levels (switches) occur only between the nearest levels. New indicators of the variability of blood saturation were proposed. These are the frequencies of saturation level switches (event intensities) and the intervals between them. It was established that these indicators are described by statistical distributions of Poisson and Erlang, respectively. Comparison of new variability indicators with the most reliable statistical – inter-quartile range – indicates that the new indicators also provide for the division of the data set into three subgroups according to the magnitude of variability. This division is statistically significant at a confidence level of 0.99 in both approaches, however, the division into sub-groups is slightly different in these methods. It was shown that the proposed indicators of the variability of SaO2 signals are scale-invariant, that is, they do not depend on the length of observation interval. This is a consequence of the fractality of the positions of differentials in the observation interval. The established switch frequencies for subgroups in order of increasing variability are (0.06, 0.11, and 0.20) Hz. These frequencies are manifested on Fourier spectra of differentials of SaO2

A Statistical Model of Fibre Distribution in a Steel Fibre Reinforced Concrete

The aim of the research was to create a model of steel fibre distribution in a Steel Fibre Reinforced Concrete space using statistical probability means. The model was created in order to better understand the behaviour of the composite under operating conditions. Four statistical distributions (Beta, Kumaraswamy, Three Parameter Beta and Generalised Transmuted Kumaraswamy) were examined to find the distribution that best described fibre settling phenomenon caused by manufacturing process conditions. In the next stage the chosen statistical distribution was adapted to create the model of steel fibre distribution in a Steel Fibre Reinforced Concrete space. The model took into account technological conditions such as vibrating time and properties such as consistency of the tested concrete. The model showed a good agreement with the real fibre distribution.

Distribution of clones among hosts for the lizard malaria parasite Plasmodium mexicanum

Background Malaria parasites reproduce asexually, leading to the production of large numbers of genetically identical parasites, here termed a clonal line or clone. Infected hosts may harbor one or more clones, and the number of clones in a host is termed multiplicity of infection (MOI). Understanding the distribution of parasite clones among hosts can shed light on the processes shaping this distribution and is important for modeling MOI. Here, I determine whether the distribution of clones of the lizard malaria parasite Plasmodium mexicanum differ significantly from statistical distributions commonly used to model MOI and logical extensions of these models. Methods The number of clones per infection was assessed using four microsatellite loci with the maximum number of alleles at any one locus used as a simple estimate of MOI for each infection. I fit statistical models (Poisson, negative binomial, zero-inflated models) to data from four individual sites to determine a best fit model. I also simulated the number of alleles per locus using an unbiased estimate of MOI to determine whether the simple (but potentially biased) method I used to estimate MOI influenced model fit. Results The distribution of clones among hosts at individual sites differed significantly from traditional Poisson and negative binomial distributions, but not from zero-inflated modifications of these distributions. A consistent excess of two-clone infections and shortage of one-clone infections relative to all fit distributions was also observed. Any bias introduced by the simple method for estimating of MOI did not appear to qualitatively alter the results. Conclusions The statistical distributions used to model MOI are typically zero-truncated; truncating the Poisson or zero-inflated Poisson yield the same distribution, so the reasonable fit of the zero-inflated Poisson to the data suggests that the use of the zero-truncated Poisson in modeling is adequate. The improved fit of zero-inflated distributions relative to standard distributions may suggest that only a portion of the host population is located in areas suitable for transmission even at small sites (<1 ha). Collective transmission of clones and premunition may also contribute to deviations from standard distributions.

The Statistical Analysis of Anisotropy Fluctuations of CMB Temperature in Angular Spatial and Temporal Areas

The changes in the nature of the statistical distributions of the anisotropy of the temperature of CMB in the satellite measurements of the “WMAP” probe were analyzed for the presence of laws in them in changes within the adjacent periods of data accumulation. Statistical distributions of changes in anisotropy between adjacent data accumulation periods were analyzed. The probability of the occurrence of such unidirectional changes at different frequencies of satellite measurements was analyzed and the probability of their occurrence under the influence of non-random factors was estimated.