Extended Generalized Sinh-Normal Distribution

Positively skewed data sets are common in different areas, and data sets such as material fatigue, reaction time, neuronal reaction time, agricultural engineering, and spatial data, among others, need to be fitted according to their features and maintain a good quality of fit. Skewness and bimodality are two of the features that data sets like this could present simultaneously. So, flexible statistical models should be proposed in this sense. In this paper, a general extended class of the sinh-normal distribution is presented. Additionally, the asymmetric distribution family is extended, and as a natural extension of this model, the extended Birnbaum–Saunders distribution is studied as well. The proposed model presents a better goodness of fit compared to the other studied models.

Max Weibull-G Power Series Distributions

Based on the Weibull-G Power probability distribution family, we have proposed a new family of probability distributions, named by us the Max Weibull-G power series distributions, which may be applied in order to solve some reliability problems. This implies the fact that the Max Weibull-G power series is the distribution of a random variable max (X1 ,X2 ,...XN) where X1 ,X2 ,... are Weibull-G distributed independent random variables and N is a natural random variable the distribution of which belongs to the family of power series distribution. The main characteristics and properties of this distribution are analyzed.

T-Inverse Exponential Family Of Distributions

Recently, several methods have been introduced to generate neoteric distributions with more exibility, like T-X, T-R [Y] and alpha power. The T-Inverse exponential [Y] neoteric family of distributons is proposed in this paper utilising the T-R [Y] method. A generalised inverse exponential (IE) distribution family has been established. The distribution family is generated using quantile functions of some dierent distributions. A number of general features in the T-IE [Y] family are examined, like mean deviation, mode, moments, quantile function, and entropies. A special model of the T-IE [Y] distribution family was one of those old distributions. Certain distribution examples are produced by the T-IE [Y] family. An applied case was presented which showed the importance of the neoteric family.

Anxiety and depression: population distribution and family associations

Aim. The aim of the study was to characterize the population distribution of psychiatric phenotypes according to anxiety and depression. Methods. The level of anxiety and depression was assessed with the HADS Hospital Anxiety and Depression Scale test. Students in grades 9-11 of secondary schools in Kharkiv, as well as their parents, were tested. We tested 306 persons from 115 families. Results. The frequency of depression among men in the Kharkiv population is 9%, among women 11%, among boys 15%, among girls 22%; the frequency of increased anxiety among men is 14%, among women 22%, among boys 19%, among girls 44%. There is a positive relationship between anxiety and depression in older men and women, expressed by the association coefficient in men rDT =0.45, in women rDT =0.79. The relatives revealed a similarity in psychological types, described by the association index for depression in mother/daughter pairs r = 0.40, mother/son r = 0.03, father/daughter r = 0.20, father/son r = 0.40; for anxiety: mother/daughter r = 0.15, mother/son r = 0.05, father/daughter r = 0.24, father/son r = 0.01. Conclusions. Individuals of the younger generation are more likely to have signs of anxiety and depression than those of their parents' generation. The parent-offspring phenotype relationship is stronger in same-sex couples compared to opposite-sex couples. Keywords: depression, anxiety, population distribution, family analysis.

Research on Volatility of Return of Chinese Stock-Market Based on Generalized Hyperbolic Distribution Family

Financial time series often present a nonlinear characteristics, and the distribution of financial data often show fat tail and asymmetry, but this don’t match with the standpoint that time series obey normal distribution of return on assets, etc, which is considered by linear parametric modeling in the traditional linear framework. This paper has a systematic introduction of the definitions of GH distribution family and related statistical characteristics, which is based on reviewing the basic properties of the ARCH/GARCH model family and a common distribution of its disturbance. And select the Shanghai Composite Index and the Shanghai and Shenzhen (CSI) 300 index daily return rate index to estimate volatility model. GH distribution is used for further fitting to disturbance. This is done after take full account of the effective extraction of the model for the disturbance distribution information. The results show that the GH distribution can effectively fitting residuals distribution of the volatility models about series on return rate.

Stochastic orders for a multivariate Pareto distribution

In this article we give some theoretical results for equivalence between different stochastic orders of some kind multivariate Pareto distribution family. Weak multivariate orders are equivalent or imply different stochastic orders between extremal statistics order of two random variables sequences. The random variables in this article are not neccesary independent.

Does the Pareto Principle describe parasite counts in humans? The case of hookworm in pregnant women

The Pareto Principle (PP) - that 80% of an attribute are found in 20% of individuals - is one way to characterize heterogeneity in infectious diseases. An alternative is the dispersion parameter (k) of the negative binomial distribution (NBD). The NBD has two parameters, while the PP is a single property which may hold for any distribution family. The objectives of the current work are: a) to obtain a relation between the PP and NBD, i.e. to specify which combinations of NBD parameters comply with the PP; b) for hookworm, a soil-transmitted intestinal parasite of humans, to identify whether the PP or the NBD is a more parsimonious description of heterogeneity of infection load. For objective a), an empirical relation is found in the form of a saw-toothed line on a plot of k against the mean, reaching an asymptote of approximately 0.24. For objective b), we estimate k and the mean from nine studies from a systematic review of hookworm in pregnant women. Seven studies had higher heterogeneity than the PP, ranging from 83:20 to 100:20: we call these super-Pareto. One study was sub-Pareto (74:20), and one was Pareto (80:20). This suggests that at least two parameters, as supplied by the NBD, are necessary to describe the heterogeneity of hookworm. The probability of reaching a target reduction in prevalence is less when there is greater aggregation, which suggests that estimating aggregation via a subsample could be worthwhile, in order to set a target coverage threshold before starting mass drug administration.

Some Notes on the Omega Distribution and the Pliant Probability Distribution Family

In 2020 Dombi and Jónás (Acta Polytechnica Hungarica 17:1, 2020) introduced a new four parameter probability distribution which they named the pliant probability distribution family. One of the special members of this family is the so-called omega probability distribution. This paper deals with one of the important characteristic “saturation” of these new cumulative functions to the horizontal asymptote with respect to Hausdorff metric. We obtain upper and lower estimates for the value of the Hausdorff distance. A simple dynamic software module using CAS Mathematica and Wolfram Cloud Open Access is developed. Numerical examples are given to illustrate the applicability of obtained results.

Epidemiology and Outcomes of Bloodstream Infections in HIV-Patients during a 13-Year Period

No data on antibiotic resistance in bloodstream infection (BSI) in people living with HIV (PLWH) exist. The objective of this study was to describe BSI epidemiology in PLWH focusing on multidrug resistant (MDR) organisms. A retrospective, single-center, observational study was conducted including all positive blood isolates in PLWH from 2004 to 2017. Univariable and multivariable GEE models using binomial distribution family were created to evaluate the association between MDR and mortality risk. In total, 263 episodes (299 isolates) from 164 patients were analyzed; 126 (48%) BSI were community-acquired, 137 (52%) hospital-acquired. At diagnosis, 34.7% of the patients had virological failure, median CD4 count was 207/μL. Thirty- and 90-day mortality rates were 24.2% and 32.4%, respectively. Thirty- and 90-day mortality rates for MDR isolates were 33.3% and 46.9%, respectively (p < 0.05). Enterobacteriaceae were the most prevalent microorganisms (29.8%), followed by Coagulase-negative staphylococci (21.4%), and S. aureus (12.7%). In BSI due to MDR organisms, carbapenem-resistant K. pneumoniae and methicillin-resistant S. aureus were associated with mortality after adjustment for age, although this correlation was not confirmed after further adjustment for CD4 < 200/μL. In conclusion, BSI in PLWH is still a major problem in the combination antiretroviral treatment era and it is related to a poor viro-immunological status, posing the question of whether it should be considered as an AIDS-defining event.