Relationship among Continuous Probability Distributions and Interpolation

Aims: The Study seeks to determine the relationship that exists among Continuous Probability Distributions and the use of Interpolation Techniques to estimate unavailable but desired value of a given probability distribution. Study Design: Statistical Probability tables for Normal, Student t, Chi-squared, F and Gamma distributions were used to compare interpolated values with statistical tabulated values. Charts and Tables were used to represent the relationships among the five probability distributions. Methodology: Linear Interpolation Technique was employed to interpolate unavailable but desired values so as to obtain approximate values from the statistical tables. The data were analyzed for interpolation of unavailable but desired values at 95% a-level from the five continuous probability distribution. Results: Interpolated values are as close as possible to the exact values and the difference between the exact value and the interpolated value is not pronounced. The table and chart established showed that relationships do exist among the Normal, Student-t, Chi-squared, F and Gamma distributions. Conclusion: Interpolation techniques can be applied to obtain unavailable but desired information in a data set. Thus, uncertainty found in a data set can be discovered, then analyzed and interpreted to produce desired results. However, understanding of how these probability distributions are related to each other can inform how best these distributions can be used interchangeably by Statisticians and other Researchers who apply statistical methods employed in practical applications.

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.

Stall Warning Strategy Based On Fast Wavelet Analysis in a Multi-Stage Axial Flow Compressor

As a reliable stall warning strategy, the fast wavelet method was introduced to successfully predict the aerodynamic instability of a multi-stage axial flow compressor. One single sensor installed at each stage is proved to be sufficient to predict the stability status in a three-stage axial flow compressor. The whole prediction strategy includes the dynamic pressure signal capture, disturbance extraction using decomposition and reconstruction via fast wavelet transform, and stall warning index calculation based on statistical probability distribution. On this premise, the first occurrence of the stall in this three-stage axial flow compressor is predicted to be within the first stage, which is consistent with the stall route captured by the eight transducers around the casing wall. Thereafter, the stall warning index is used to monitor the stability status during the continuous throttling process. Furthermore, the validation using tip air injection and inlet radial distortion indicated that the stall warning index decreases as the compressor's stability improves. Conversely, the deterioration of stability causes the increase of the stall warning index. Thus, experimental results demonstrate that the stall warning method based on fast wavelet analysis can predict the aerodynamic instability in actual application.

Identifying unfamiliar voices: the influence of sample duration and parade size.

Voice identification parades can be unreliable due to the error-prone nature of earwitness responses. Home Office guidelines (2003) recommend that voice parades should consist of nine-voices, each played for 60-seconds. This makes parades resource-consuming to construct. In the present paper we conducted two experiments to see if voice parade procedures could be simplified. In Experiment 1, we investigated if reducing the duration of the voice samples on a nine-voice parade would negatively affect performance. In Experiment 2, we first explored if the same sample duration conditions used in Experiment 1 would lead to different outcomes if a six-voice parade were used. Following this, we investigated if there were any difference in identification performance based solely on whether a nine-voice (Experiment 1) or six-voice (Experiment 2) parade was used. Overall, the results suggest that voice durations can be safely reduced without disrupting listener performance. Performance on target-absent parades – which simulate an innocent suspect being apprehended – were at chance-levels in both parade sizes, but the increased number of foils in the nine-voice parade offers increased protection to an innocent suspect by virtue of statistical probability. Thus, we argue that the Home Office guidelines recommending a parade with nine-voices should be maintained.

Forecasting the effectiveness of the enterprise to intensify innovation and investment development, taking into account the financial component of economic potential

The study is devoted to the problem of analysis and forecasting of the effectiveness of the results of enterprises to ensure production and economic reserves to intensify innovation and investment development in the context of monitoring the state of their economic potential. It is the basis for the formation of endogenous and exogenous capabilities of the enterprise, aimed at achieving targeted results in each area of its activities. Creating favorable conditions for economic growth of enterprises based on the intensification of innovation and investment development requires the effective implementation of production programs using the financial component of economic potential. Based on the analysis of methodological tools for evaluating the activities of a mining and processing enterprise, formed a comprehensive methodology for quantitative and qualitative assessment of actual and projected values of performance indicators of the enterprise. It is based on determining the statistical probability of achieving a positive level of the indicator, the probability of its falling into a given interval of deviation from the recommended allowable values and an integrated assessment of the financial component of economic potential. Approbation of the developed technique is carried out within the limits of the express analysis of effective indicators of efficiency of activity of mining and processing enterprises. The results showed that with high reliability of the forecast (more than 0.85), the recommended values of the level of margin to achieve the desired efficiency are in the range of 8÷10 %. Within a sufficient level of reliability of the forecast (not less than 0.75), the recommended values of this margin are 10÷24 %. In this case, the integrated indicator of the assessment of the financial component should be more than 0.3

Statistical Floquet prethermalization of the Bose-Hubbard model

The manipulation of many-body systems often involves time-dependent forces that cause unwanted heating. One strategy to suppress heating is to use time-periodic (Floquet) forces at large driving frequencies. For quantum spin systems with bounded spectra, it was shown rigorously that the heating rate is exponentially small in the driving frequency. Recently, such exponential suppression of heating has been observed in an experiment with ultracold atoms, realizing a periodically driven Bose-Hubbard model. This model has an unbounded spectrum and, hence, is beyond the reach of previous theoretical approaches. Here, we study this model with two semiclassical approaches valid, respectively, at large and weak interaction strengths. In both limits, we compute the heating rates by studying the statistical probability to encounter a many-body resonance, and obtain a quantitative agreement with the exact diagonalization of the quantum model. Our approach demonstrates the relevance of statistical arguments to Floquet perthermalization of interacting many-body quantum systems.

Changes in psychophysiological indicators of students due to implementation of individual and motivational levels of the swimming training system

The reliability of the scientific research results is largely determined by the level of adequacy of selection and the complexity of the application of methods and means that provide pedagogical influences on the students‟ body. Purpose: to establish changes in the psychophysiological indicators of higher educational institution students (boys and girls) based on the results of the implementation of training programs at different individual and motivational levels of the swimming training system. Material and methods. To the study involved students (boys and girls) aged 18-20 years old, who studied at Kherson State University during 2020-2021 academic year. The contingent of students was: 1EG, n = 28 boys and 23 girls; 2EG, n = 25 boys and 26 girls; 3EG, n = 21 boys and 23 girls; 4EG, n = 23 boys and 21 girls; CG, n = 32 boys and 29 girls. Results. During the implementation of classes program of different methodological content at different individual and motivational levels of swimming training system of higher educational institution students (boys and girls) in all groups without exception recorded statistically significant internal changes in psychophysiological indicators, mostly in percentage values and statistical probability (boys and girls) of the control group. Conclusions. Improving the strength of nervous processes in the structure of psychophysiological readiness of student youth indicates the promotion of domestic and professional activities. This also indicates a fact that the implementation of training programs at different individual and motivational levels of swimming training system has a positive effect on psychophysiological qualities, reactions, variants of complex visual and motor reaction and tapping test indirectly indicates the acquisition of abilities to general performance.

Using the Semantic Information G Measure to Explain and Extend Rate-Distortion Functions and Maximum Entropy Distributions

In the rate-distortion function and the Maximum Entropy (ME) method, Minimum Mutual Information (MMI) distributions and ME distributions are expressed by Bayes-like formulas, including Negative Exponential Functions (NEFs) and partition functions. Why do these non-probability functions exist in Bayes-like formulas? On the other hand, the rate-distortion function has three disadvantages: (1) the distortion function is subjectively defined; (2) the definition of the distortion function between instances and labels is often difficult; (3) it cannot be used for data compression according to the labels’ semantic meanings. The author has proposed using the semantic information G measure with both statistical probability and logical probability before. We can now explain NEFs as truth functions, partition functions as logical probabilities, Bayes-like formulas as semantic Bayes’ formulas, MMI as Semantic Mutual Information (SMI), and ME as extreme ME minus SMI. In overcoming the above disadvantages, this paper sets up the relationship between truth functions and distortion functions, obtains truth functions from samples by machine learning, and constructs constraint conditions with truth functions to extend rate-distortion functions. Two examples are used to help readers understand the MMI iteration and to support the theoretical results. Using truth functions and the semantic information G measure, we can combine machine learning and data compression, including semantic compression. We need further studies to explore general data compression and recovery, according to the semantic meaning.

‘Masha shila plat’e…’ ‒ Some Facts on Lexical Indicators of the Semantics of Biological Sex in Russian

The article deals with the lexical means expressing the biological sex semantics in Russian. Nouns, adjectives, verbs, adverbs may carry information on the denotatum of the semantically related noun. According to the National corpus of Russian language a set of such relevant lexemes and the statistical probability of their male and female markedness is established. Also the statistical probability of their male and female markedness in accordance with the modern Russian lexical minimum is determined.

"˜Regression toward the mean" in replications of fundamental research studies on homeopathic high potencies?

Around 100 high-potency studies, each one replicating earlier studies, were located in a bibliometric study on fundamental research [1]. 70% of the replication studies yielded the same result as the original study, 10% the opposite result, and 20% found no difference between the test and control groups. This is to say, the final standing was 70 positive, 10 negative and 20 undecided results. Among the replication studies performed by the original laboratory, the outcomes were 83 positive and 5 negative (12 undecided); in the ones performed in laboratories of independent researchers invited to participate in a multicentric study the corresponding outcomes were 75 and 11 (14), and the ones of studies performed by external researchers 48 and 14 (38). Had the experiments been performed on purely random phenomena the most probable outcomes would have been 33 : 33 : 33. In a follow-up study we sought to establish whether the outcomes of the replication studies might be attributed to regression toward the means. As is known, this term describes the situation in which a random experiment yields an extreme result, while subsequent replications give average results quite independent from the initial one. By contrast, when the experiment is not entirely based entirely on chance, subsequent replications tend to yield results that deviate from the average in the same direction as the initial one. We thus grouped the studies into 3 clusters of at least 7 articles according to their date of publication. The relative frequencies of positive, undecided and negative results were graphically represented through by curves to allow for visual comparison of the initial result versus the results of the replication studies for each of the 3 clusters. Regression towards the mean was neither observed in the results of the replication studies taken together nor in the group of laboratory-internal replication studies. By contrast, the group of multicentric replication studies exhibited increase of the relative frequency of undecided results and decrease of the one of positive results. In the group of external replication studies the relative frequency of undecided results increased and the one of positive and of negative results decreased. The statistical probability of drawing a ‘positive result’ from a total of 3 equally probable options (positive, undecided, negative) is 33.3%. By contrast, within the entirety of replication studies the frequency of positive results was 77% on the first replication, 66.7% on the second and 66.7% on the third. Unlike the results from the group of laboratory-internal studies, the ones of multicentric and external replications are suggestive of regression towards the mean. However the magnitude of this effect is far weaker than would be expected from a purely random distribution of results. One question that remains is why there appears to have been practically no regression in the laboratory-internal replications. This should not be cheaply attributed to publication bias. Especially in experiments on homoeopathic high potencies, it could well be that numerous, in some part hidden factors of influence are involved, which internal laboratories – possibly unwittingly through unreflected working habits– are better at controlling than external laboratories, regardless of the effort invested to this end. Keywords: high dilution, replication experiments, regression to the mean References [1] Endler PC, Bellavite P, Bonamin L, Jäger T. Mazon S. Replications of fundamental research models in ultra high dilutions, 1994 and 2015: an update on a bibliometric study. Homeopathy 2015;104:235-245