univariate distribution
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Forecasting ◽  
2021 ◽  
Vol 4 (1) ◽  
pp. 51-71
Author(s):  
Arne Vogler ◽  
Florian Ziel

The present paper considers the problem of choosing among a collection of competing electricity price forecasting models to address a stochastic decision-making problem. We propose an event-based evaluation framework applicable to any optimization problem, where uncertainty is captured through ensembles. The task of forecast evaluation is simplified from assessing a multivariate distribution over prices to assessing a univariate distribution over a binary outcome directly linked to the underlying decision-making problem. The applicability of our framework is demonstrated for two exemplary profit-maximization problems of a risk-neutral energy trader, (i) the optimal operation of a pumped-hydro storage plant and (ii) the optimal trading of subsidized renewable energy in Germany. We compare and contrast the approach with the full probabilistic and profit–loss-based evaluation frameworks. It is concluded that the event-based evaluation framework more reliably identifies economically equivalent forecasting models, and in addition, the results suggest that an event-based evaluation specifically tailored to the rare event is crucial for decision-making problems linked to rare events.


2021 ◽  
Vol 71 (6) ◽  
pp. 1581-1598
Author(s):  
Vahid Nekoukhou ◽  
Ashkan Khalifeh ◽  
Hamid Bidram

Abstract The main aim of this paper is to introduce a new class of continuous generalized exponential distributions, both for the univariate and bivariate cases. This new class of distributions contains some newly developed distributions as special cases, such as the univariate and also bivariate geometric generalized exponential distribution and the exponential-discrete generalized exponential distribution. Several properties of the proposed univariate and bivariate distributions, and their physical interpretations, are investigated. The univariate distribution has four parameters, whereas the bivariate distribution has five parameters. We propose to use an EM algorithm to estimate the unknown parameters. According to extensive simulation studies, we see that the effectiveness of the proposed algorithm, and the performance is quite satisfactory. A bivariate data set is analyzed and it is observed that the proposed models and the EM algorithm work quite well in practice.


PeerJ ◽  
2021 ◽  
Vol 9 ◽  
pp. e12327
Author(s):  
Weiwen Zhao ◽  
Wenjun Liang ◽  
Youzhi Han ◽  
Xi Wei

Larix principis-rupprechtii is an important and widely distributed species in the mountains of northern China. However, it has inefficient natural regeneration in many stands and difficulty recruiting seedlings and saplings. In this study, we selected six plots with improved naturally-regenerated L. principis-rupprechtii seedlings. A point pattern analysis (pair-correlation function) was applied to identify the spatial distribution pattern and correlation between adult trees and regenerated seedlings mapped through X/Y coordinates. Several possible influencing factors of L. principis-rupprechtii seedlings’ natural regeneration were also investigated. The results showed that the spatial distribution patterns of Larix principis-rupprechtii seedlings were concentrated 0–5 m around adult trees when considering the main univariate distribution type of regeneration. There was a positive correlation at a scale of 1.5–4 m between seedlings and adult trees according to bivariate analyses. When the scale was increased, these relationships were no longer significant. Generally, adult trees raised regenerated L. principis-rupprechtii seedlings at a scale of 1.5–4 m. Principal component analysis showed that the understory herb diversity and litter layer had a negative correlation with the number of regenerated seedlings. There was also a weak relationship between regenerated numbers and canopy density. This study demonstrated that the main factors promoting natural regeneration were litter thickness, herb diversity, and the distance between adult trees and regenerated seedlings. Additionally, these findings will provide a basis for the late-stage and practical management of natural regeneration in northern China’s mountain ranges.


2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Martin Treppner ◽  
Adrián Salas-Bastos ◽  
Moritz Hess ◽  
Stefan Lenz ◽  
Tanja Vogel ◽  
...  

AbstractDeep generative models, such as variational autoencoders (VAEs) or deep Boltzmann machines (DBMs), can generate an arbitrary number of synthetic observations after being trained on an initial set of samples. This has mainly been investigated for imaging data but could also be useful for single-cell transcriptomics (scRNA-seq). A small pilot study could be used for planning a full-scale experiment by investigating planned analysis strategies on synthetic data with different sample sizes. It is unclear whether synthetic observations generated based on a small scRNA-seq dataset reflect the properties relevant for subsequent data analysis steps. We specifically investigated two deep generative modeling approaches, VAEs and DBMs. First, we considered single-cell variational inference (scVI) in two variants, generating samples from the posterior distribution, the standard approach, or the prior distribution. Second, we propose single-cell deep Boltzmann machines (scDBMs). When considering the similarity of clustering results on synthetic data to ground-truth clustering, we find that the $$scVI_{posterior}$$ s c V I posterior variant resulted in high variability, most likely due to amplifying artifacts of small datasets. All approaches showed mixed results for cell types with different abundance by overrepresenting highly abundant cell types and missing less abundant cell types. With increasing pilot dataset sizes, the proportions of the cells in each cluster became more similar to that of ground-truth data. We also showed that all approaches learn the univariate distribution of most genes, but problems occurred with bimodality. Across all analyses, in comparing 10$$\times$$ × Genomics and Smart-seq2 technologies, we could show that for 10$$\times$$ × datasets, which have higher sparsity, it is more challenging to make inference from small to larger datasets. Overall, the results show that generative deep learning approaches might be valuable for supporting the design of scRNA-seq experiments.


2021 ◽  
Author(s):  
Zahra Fahimirad ◽  
Nazanin Shahkarami

Abstract Climate change has made many alterations to the Earth's climate, including hydro-climatic extreme events. For investigating the effect of climate change on hydro-meteorological droughts in the Kamal-Saleh dam basin in Markazi province, Iran, a new and comprehensive index was developed for accurate estimation of drought in a more realistic condition, for future climate conditions. This aggregate drought index (ADI) represents the main characteristics of meteorological and hydrological drought. Temperature and precipitation projections for future climates were simulated by five CMIP5 models and downscaled over the study area for the periods of 2050s (2040-2069) and 2080s (2070-2099) relative to the baseline period (1976-2005). By fitting five univariate distribution functions on drought severity and duration, proper marginal distributions were selected. The joint distribution of drought severity and duration was chosen from five types of copula functions. The results revealed that severe droughts are expected to occur frequently in a shorter period in the future.


Psychology ◽  
2021 ◽  
Author(s):  
Zhiyong Zhang ◽  
Wen Qu

In statistics, kurtosis is a measure of the probability distribution of a random variable or a vector of random variables. As mean measures the centrality and variance measures the spreadness of a probability distribution, kurtosis measures the tailedness of the distribution. Kurtosis for a univariate distribution was first introduced by Karl Pearson in 1905. Kurtosis, together with skewness, is widely used to quantify the non-normality—the deviation from a normal distribution—of a distribution. In psychology, kurtosis has often been studied in the field of quantitative psychology to evaluate its effects on psychometric models.


PLoS ONE ◽  
2020 ◽  
Vol 15 (12) ◽  
pp. e0244335
Author(s):  
K. M. Mustafizur Rahman ◽  
Md. Ismail Tareque

Background Smoking cigarette/bidi, is a serious health threat, causes preventable premature morbidity and mortality. Higher prevalence of smoking among the youth hampers a country’s development, as the youth are the main drivers of socio-economic development. An effective understanding of factors associated with youth smoking is precious to prevent youth smoking. This study aims to identify the determinants of smoking cigarette/bidi among the youth male of the rural areas of Mymensingh district in Bangladesh. Methods The primary data from the project “Knowledge, awareness and practices among youth smokers in Trishal Upazila under Mymensingh district: A micro-survey study”, funded by the Research and Extension Center, Jatiya Kabi Kazi Nazrul Islam University, Bangladesh was utilized in the current study. The data consists of 385 youth males aged 15–24 years who were interviewed face-to-face from the rural areas of Mymensingh district in Bangladesh. Univariate distribution, chi-square tests, and binary logistic regression model were employed to identify the factors associated with smoking cigarette/bidi among the youth male. Results The prevalence of smoking cigarette/bidi among the youth male is 40.3% [95% CI: 35.0%-45.0%]. Age, occupation, monthly income, family’s monthly income, cigarette/bidi smoking status of father, brother and close friends, and knowledge about harmfulness of smoking are revealed as the determinants of cigarette/bidi smoking. For instance, the odds of being smoker increases with the increase in age (Odds ratio [OR]: 1.33 [1.17–1.51]). Business owner is less likely (OR: 0.15 [0.03–0.68]) to smoke than the day labourer. Having smoker fathers (OR: 2.51 [1.39–4.53]), smoker brothers (OR: 2.88 [1.39–5.96]), smoker friends (OR: 9.85 [5.85–1.27]) are significantly associated with smoking cigarette/bidi. Conclusion As the first study, it provides the determinants of cigarette/bidi smoking among youth male of the rural areas of Mymensingh district in Bangladesh. Relevant authorities are suggested to consider the study’s findings and recommendations to revise the existing smoking policies so that smoking among youth can be prevented for future development of the country.


2020 ◽  
Author(s):  
Martin Treppner ◽  
Adrián Salas-Bastos ◽  
Moritz Hess ◽  
Stefan Lenz ◽  
Tanja Vogel ◽  
...  

ABSTRACTDeep generative models, such as variational autoencoders (VAEs) or deep Boltzmann machines (DBM), can generate an arbitrary number of synthetic observations after being trained on an initial set of samples. This has mainly been investigated for imaging data but could also be useful for single-cell transcriptomics (scRNA-seq). A small pilot study could be used for planning a full-scale study by investigating planned analysis strategies on synthetic data with different sample sizes. It is unclear whether synthetic observations generated based on a small scRNA-seq dataset reflect the properties relevant for subsequent data analysis steps.We specifically investigated two deep generative modeling approaches, VAEs and DBMs. First, we considered single-cell variational inference (scVI) in two variants, generating samples from the posterior distribution, the standard approach, or the prior distribution. Second, we propose single-cell deep Boltzmann machines (scDBM). When considering the similarity of clustering results on synthetic data to ground-truth clustering, we find that the scVIposterior variant resulted in high variability, most likely due to amplifying artifacts of small data sets. All approaches showed mixed results for cell types with different abundance by overrepresenting highly abundant cell types and missing less abundant cell types. With increasing pilot dataset sizes, the proportions of the cells in each cluster became more similar to that of ground-truth data. We also showed that all approaches learn the univariate distribution of most genes, but problems occurred with bimodality. Overall, the results showed that generative deep learning approaches might be valuable for supporting the design of scRNA-seq experiments.


2020 ◽  
Vol 9 (3) ◽  
pp. 36
Author(s):  
Gholamhossein G. Hamedani ◽  
Shirin Nezampour

MirMostafaee et al. (2019) proposed a continuous univariate distribution called Exponentiated Generalized Power Lindley (EGPL) distribution and studied certain properties and applications of their distribution. Akdogan et al. (2019) introduced a discrete distribution called Geometric-Zero Truncated Poisson (GZTP) distribution and provided its properties and applications. The present short note is intended to complete, in some way, the works cited above via establishing certain characterizations of the EGPL and GZTP distributions in different directions.


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