Methods of Estimating the Form of the Probability Distribution Density in Tasks of Processing Measurement Results

Issues associated with methods for estimating the shape of the probability distribution density curve are analyzed in order to classify them when processing measurement results. For example, such nonparametric methods as the method of histograms and frequency polygon, as well as the method of classification of distributions, are considered. It is shown that the values of the anticurtosis and entropy coefficient can be taken as independent features of the form of symmetric distributions. For probability distribution densities that have a one-sided character, such as multiplicative noise, a skewness coefficient should be added to the parameters to consider. Recurrent procedures for obtaining current estimates of numerical characteristics of analyzed random processes are given. The results of processing a random process based on recurrent procedures are presented. It is shown that when the number of samples increases, the estimates obtained by using recurrent and non-recurrent procedures converge. The scattering of estimates of probability distribution density parameters, such as variance, relative mean square error, and entropy error, is determined.

Assessment of medical and pharmaceutical waste flows during the coronavirus pandemic in the Rabat-Sale-Kenitra region, Morocco

The COVID-19 pandemic has created unprecedented difficulties for health care institutions, which are required to manage not only the flow of patients with COVID-19, but also the management of medical and pharmaceutical waste (MPW). At the level of Morocco, the waste produced by hospitals has risen sharply in the regions most affected by the virus, such as the Rabat-Sale-Kenitra region (15.05% of recorded cases). The objective of this study is to perform a descriptive statistical analysis and to evaluate the generation rates of MPW generated during the treatment of the coronavirus pandemic, with reference to a large health care hospital in the region, in order to enable decision-makers to adopt responses in terms of regular and continuous management of MPW. The Moulay Abdellah hospital in Sale has a bedding capacity allocated to the COVID-19 patient of 110 beds with a Average Occupation Rate (AOR) of 100% and an average production of 13tons per month. The study showed that the average rate of MPW generated is 4 kg per bed per day, which is twice as high as the average generation rate during normal operation in 2019. As well, frequency analysis of the data revealed that MPW generation follows a log normal distribution with a correlation coefficient of 0.9. The distribution is skewed to the right and flatter than the normal distribution curve as judged by the skewness coefficient which is 0.87 and kurtosis coefficient which has a value of 1.286, indicating a deviation from normality.

A Qualitative Study of Time Overrun of Completed Road Projects Awarded by the Niger Delta Development Commission in the Niger Delta Region of Nigeria

Time overrun of completed road projects awarded by the Niger Delta Development Commission (NDDC) in the Niger Delta Region of Nigeria from its inception in 2000 up to 2015 was studied. Out of 3315 roads awarded, only 1081 roads representing 31.65 percent were completed within the review period. The qualitative study was carried out on randomly selected completed 162 road projects for analysis, and a conceptual model of time series was developed. In developing the regression model, both dependent and independent variables were subjected to normality tests assessed by skewness coefficient, kurtosis value, Jarque-Bera test, residual probability plot, heteroscedasticity test and the variance inflation factor. Also, with knowledge of total road projects awarded by the Commission, it is now possible to predict proportions of roads experiencing schedule overruns.

MINIMAL WATER RUNOFF OF THE AZOV RIVER BASIN AREA DURING SUMMER-AUTUMN AND WINTER LOW-WATER PERIODS

For the purpose of value and analysis of the statistical characteristics of low-water runoff during summer-autumn and winter low flow periods on the rivers of the Priazov’s, used the time series of the minimum runoff of the rivers by 16 WGS during the period of from beginning observation till 2015 inclusive. In order to protect the water resources in the region, it is necessary to use its rationale, especially during low water periods than are minimal water discharges. For these aims, It is necessary to estimate the values of the characteristics of the minimum runoff in the Priazov region on the modern initial data, which is relevant, both in scientific and practical terms. Before generalizing the mean runoff modules in the summer-autumn and winter periods, the influence of local factors (latitudinal position, aforestation, and swampy watersheds) on their value was investigated. No significant influence of local factors was revealed, except for a good relationship with the latitude of the catchment centers. To determine the minimum runoff in winter for unexplored rivers of the territory, a map of isolines of 30-day minimum runoff modules is proposed. The distribution over the territory is uneven and varies from 0.30 l / (s • km2) in the southwestern part of the territory to 3.25 l / (s • km2) in the northeastern parts. The isolines are drawn with a step of 0.20 l / (s • km2). The map error is ± 4.3%, which corresponds to the accuracy of the initial information and the requirements of the current regulatory document SNiP 2.10.14-83. In the summer-autumn period, the distribution over the territory of the average minimum runoff modules is similar – in the south (in the Molochnaya river basin) low values are observed from 0.080 l / (s • km2), significantly increases in the northeast direction to 2.50 l / (s • km2) in the Kripenʹka river basin. Isolines are also drawn with a step of 0.20 l / (s • km2). The error in determining the minimum runoff in the summer-autumn period according to the proposed map is slightly higher and amounts to ± 7.7%, but it also meets the requirements for the accuracy of calculating the low-water runoff. To determine the coefficients of variability of low-water runoff, the obtained regional calculation equations, the accuracy of the calculation for which is provided by significant correlation coefficients; the skewness coefficient is normalized in relation to the coefficient of variation at the 2.0 level. The proposed regional method for determining the value of the minimum runoff for the summer-autumn and winter periods makes it possible to use it without modifications in order to reliably substantiate the runoff characteristics during the dry season on the Priazov rivers.

ESTIMATION OF THE T-YEAR SPECIFIC DISCHARGE USING THE REGIONALISED SKEWNESS COEFFICIENT OF THE LOG-PEARSON TYPE III DISTRIBUTION

In this paper the results are presented of estimation of T-year specific discharge of several streams in two regions in Slovakia. The Qmax time series used in the study were observed at water gauges from lowland Slovak part of the Morava River basin, and from the mountainous Belá River basin. For estimating the design values, we have studied the use of only one type of probability distribution, namely the Log-Pearson Type III Distribution (LP3 distribution). The use of only one type of distribution brings several benefits, e.g. possibility of the regionalization of the distribution parameters (in this study skew coefficient). In the first step the design values of the specific discharge series qmax (with historical data) were estimated and regional skew coefficients Gr of the LP3 distribution were computed. Regional skewness coefficient Gr was estimated to be 0.38 in the Morava River region, and 0.73 in the Belá River region. In many cases the estimate of the 1000-year specific discharge is two times higher than the value of the 100-year specific discharge. Then we have derived the empirical relations between station skew coefficient G and the elevation of the water gauge. In the second step we have derived the empirical relationships between 1000-years specific discharge q1000 and the elevation of the water gauge for both regions separately. The derived empirical regional equations can be used to estimate the 1000-years specific discharge of other streams in the region.

Quantitative laboratory results: normal or lognormal distribution?

The identification of a suitable distribution model is a prerequisite for the parametric estimation of reference intervals and other statistical laboratory tasks. Classification of normal vs. lognormal distributions from healthy populations is easy, but from mixed populations, containing unknown proportions of abnormal results, it is challenging. We demonstrate that Bowley’s skewness coefficient differentiates between normal and lognormal distributions. This classifier is robust and easy to calculate from the quartiles Q1–Q3 according to the formula (Q1 − 2 · Q2 + Q3)/(Q3 − Q1). We validate our algorithm with a more complex procedure, which optimizes the exponent λ of a power transformation. As a practical application, we show that Bowley’s skewness coefficient is suited selecting the adequate distribution model for the estimation of reference limits according to a recent International Federation of Clinical Chemistry and Laboratory Medicine (IFCC) recommendation, especially if the data is right-skewed.

Regionalization of potential evapotranspiration using a modified region of influence

This study examined the effect of different attributes on regionalization of potential evapotranspiration (ETp) in Urmia Lake Basin (ULB), Iran, using the region of influence (RoI) framework. Data for the period 1997–2016 from 30 weather stations were selected for the analysis. To achieve similarity between stations, climate, geographical, and statistical attributes were selected. To determine the effect of each attribute, the Shannon entropy weighting method was used. The results showed that attribute weighting had a significant impact on ETp clustering. Among the groups studied, the most significant effect of weighting was observed in the statistical attributes category. Among all attributes, skewness coefficient (CS) was the most useful in determining similarity between stations. Based on the results, ULB can be divided into three homogeneous regions. Proximity of weather stations did not always indicate similarity between them, but by weighting the stations in addition to weighting the attributes, more accurate estimates of ETp in the basin were obtained. Overall, the results demonstrate potential for application of the RoI approach in regionalization of ETp, by assigning a weight to weather stations and to influencing attributes.

Use of Nonconventional Dispersion Measures to Improve the Efficiency of Ratio-Type Estimators of Variance in the Presence of Outliers

The use of auxiliary information in survey sampling to enhance the efficiency of the estimators of population parameters is a common phenomenon. Generally, the ratio and regression estimators are developed by using the known information on conventional parameters of the auxiliary variables, such as variance, coefficient of variation, coefficient of skewness, coefficient of kurtosis, or correlation between the study and auxiliary variable. The efficiency of these estimators is dubious in the presence of outliers in the data and a nonsymmetrical population. This study presents improved variance estimators under simple random sampling without replacement with the assumption that the information on some nonconventional dispersion measures of the auxiliary variable is readily available. These auxiliary variables can be the inter-decile range, sample inter-quartile range, probability-weighted moment estimator, Gini mean difference estimator, Downton’s estimator, median absolute deviation from the median, and so forth. The algebraic expressions for the bias and mean square error of the proposed estimators are obtained and the efficiency conditions are derived to compare with the existing estimators. The percentage relative efficiencies are used to numerically compare the results of the proposed estimators with the existing estimators by using real datasets, indicating the supremacy of the suggested estimators.

Skewness of Maximum Likelihood Estimators in the Weibull Censored Data

In this paper, we obtain a matrix formula of order n − 1 / 2 , where n is the sample size, for the skewness coefficient of the distribution of the maximum likelihood estimators in the Weibull censored data. The present result is a nice approach to verify if the assumption of the normality of the regression parameter distribution is satisfied. Also, the expression derived is simple, as one only has to define a few matrices. We conduct an extensive Monte Carlo study to illustrate the behavior of the skewness coefficient and we apply it in two real datasets.

Arrhythmia Classification Based on Multiple Features Fusion and Random Forest Using ECG

Cardiovascular diseases have become more and more prominent in recent years, which have proven to be a major threat to people's health. Accurate detection of arrhythmia in patients has important implications for clinical treatment. The aim of this study was to propose a novel automatic classification method for arrhythmia in order to improve classification accuracy. The electrocardiogram (ECG) signal was subjected preprocessing for denoising purposes using a wavelet transform. Then, the local and global characteristics of the beat, which contained RR interval features according with the clinical diagnosis criterion, morphology features based on wavelet packet decomposition and statistical features along with kurtosis coefficient, skewness coefficient and variance are exploited and fused. Meanwhile, the dimensionality of wavelet packet coefficients were reduced via principal component analysis (PCA). Finally, these features were used as the input of the random forest classifier to train the model and were then compared with the support vector machine (SVM) and back propagation (BP) neural networks. Based on 100,647 beats from the MIT-BIH database, the proposed method achieved an average accuracy, specificity and sensitivity of 99.08%, 99.00% and 89.31%, respectively, using the intra-patient beats, and 92.31%, 89.98% and 37.47%, respectively, using the inter-patient beats. Moreover, two classification schemes, namely, inter-patient and intra-patient scheme, were validated. Compared with the other methods referred to in this paper, the performance of the novel method yielded better results.