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A Non-Parametric Estimation Method of the Population Size in Capture-Recapture Experiments With Right Censored Data 右截尾数据捕获-再捕获实验中种群大小的非参数估计方法
IF 1.5 3区 环境科学与生态学
Environmetrics Pub Date : 2025-04-02 DOI: 10.1002/env.70013
Anabel Blasco-Moreno, Pedro Puig
{"title":"A Non-Parametric Estimation Method of the Population Size in Capture-Recapture Experiments With Right Censored Data","authors":"Anabel Blasco-Moreno,&nbsp;Pedro Puig","doi":"10.1002/env.70013","DOIUrl":"https://doi.org/10.1002/env.70013","url":null,"abstract":"<div>\u0000 \u0000 <p>We present a new non-parametric approach for estimating the total number of animals or species when we only have information on the number of animals or species \u0000 that have been observed once, twice, <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>…</mi>\u0000 </mrow>\u0000 <annotation>$$ dots $$</annotation>\u0000 </semantics></math>, and the number of animals or species that have been observed <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>r</mi>\u0000 </mrow>\u0000 <annotation>$$ r $$</annotation>\u0000 </semantics></math> and more than <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>r</mi>\u0000 </mrow>\u0000 <annotation>$$ r $$</annotation>\u0000 </semantics></math> times. The approach, like the Chao estimator, gives a lower bound on population size while also providing bootstrap confidence intervals. We conducted simulations to compare our estimator to other competing ones in special scenarios with <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>r</mi>\u0000 <mo>=</mo>\u0000 <mn>2</mn>\u0000 </mrow>\u0000 <annotation>$$ r=2 $$</annotation>\u0000 </semantics></math> and 3 and found that it performed quite well. In the case of uncensored samples, we analyze which censoring point is preferable in specific examples, as well as when censoring at <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>r</mi>\u0000 <mo>=</mo>\u0000 <mn>3</mn>\u0000 </mrow>\u0000 <annotation>$$ r=3 $$</annotation>\u0000 </semantics></math> is superior to censoring at <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>r</mi>\u0000 <mo>=</mo>\u0000 <mn>2</mn>\u0000 </mrow>\u0000 <annotation>$$ r=2 $$</annotation>\u0000 </semantics></math>.</p>\u0000 </div>","PeriodicalId":50512,"journal":{"name":"Environmetrics","volume":"36 3","pages":""},"PeriodicalIF":1.5,"publicationDate":"2025-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143761959","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"环境科学与生态学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
From Climate Chat to Climate Shock: Non-Linear Impacts of Transition Risk in Energy CDS Markets 从气候聊天到气候冲击:能源CDS市场转型风险的非线性影响
IF 1.5 3区 环境科学与生态学
Environmetrics Pub Date : 2025-04-01 DOI: 10.1002/env.70012
Emanuele Campiglio, Luca De Angelis, Paolo Neri, Ginevra Scalisi
{"title":"From Climate Chat to Climate Shock: Non-Linear Impacts of Transition Risk in Energy CDS Markets","authors":"Emanuele Campiglio,&nbsp;Luca De Angelis,&nbsp;Paolo Neri,&nbsp;Ginevra Scalisi","doi":"10.1002/env.70012","DOIUrl":"https://doi.org/10.1002/env.70012","url":null,"abstract":"<p>It is still unclear to what extent transition risks are being internalized by financial investors. In this paper, we provide a novel investigation of the impact of media-based measures of transition risks on the credit risk of energy companies, as measured by their credit default swaps (CDS) indices. We include both European and North American markets in the 2010–2020 period. Using linear and non-linear local projections, we find that a transition risk shock affects CDS indices only when combined with tangible physical climate-related impacts. We also find evidence of non-linear cross-border effects, with North American energy companies particularly affected by European dynamics. We suggest that the public reaction in the wake of severe climate-related disasters, which might push policymakers to adopt more decisive climate action, contributes to making the transition-related debate salient in the eyes of credit market actors.</p>","PeriodicalId":50512,"journal":{"name":"Environmetrics","volume":"36 3","pages":""},"PeriodicalIF":1.5,"publicationDate":"2025-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/env.70012","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143749465","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"环境科学与生态学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Effects of Climate Change on House Prices in Outdoor Tourism Destinations: A Case Study of Southwestern Colorado 气候变化对户外旅游目的地房价的影响——以美国科罗拉多州西南部为例
IF 1.5 3区 环境科学与生态学
Environmetrics Pub Date : 2025-03-24 DOI: 10.1002/env.70007
Kadie S. Clark, J. Isaac Miller
{"title":"Effects of Climate Change on House Prices in Outdoor Tourism Destinations: A Case Study of Southwestern Colorado","authors":"Kadie S. Clark,&nbsp;J. Isaac Miller","doi":"10.1002/env.70007","DOIUrl":"https://doi.org/10.1002/env.70007","url":null,"abstract":"<div>\u0000 \u0000 <p>We estimate the historical effects of climate change on real estate prices in the San Juan Mountain Region of Southwestern Colorado, an area strongly influenced by outdoor recreation-based tourism, and we use these estimates to make projections for future house prices in the region based on multiple anthropogenic climate forcing scenarios. We find that local warm-season minimum and cold-season temperature and local warm-season maximum temperature have significantly positive long-run relationships with global anthropogenic climate forcing. Moreover, once we control for non-climate factors that affect the housing market, we find that local cold-season precipitation and local warm-season maximum temperature have significant but opposite effects on local house prices. Scenario-based projections suggest that these two effects largely negate each other under any climate scenario, so that effects of climate change on house prices are expected to continue through the end of the century as they have over the past few decades.</p>\u0000 </div>","PeriodicalId":50512,"journal":{"name":"Environmetrics","volume":"36 3","pages":""},"PeriodicalIF":1.5,"publicationDate":"2025-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143690027","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"环境科学与生态学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Joint Modeling of Wind Speed and Wind Direction Through a Conditional Approach 基于条件法的风速和风向联合建模
IF 1.5 3区 环境科学与生态学
Environmetrics Pub Date : 2025-03-23 DOI: 10.1002/env.70011
Eva Murphy, Whitney Huang, Julie Bessac, Jiali Wang, Rao Kotamarthi
{"title":"Joint Modeling of Wind Speed and Wind Direction Through a Conditional Approach","authors":"Eva Murphy,&nbsp;Whitney Huang,&nbsp;Julie Bessac,&nbsp;Jiali Wang,&nbsp;Rao Kotamarthi","doi":"10.1002/env.70011","DOIUrl":"https://doi.org/10.1002/env.70011","url":null,"abstract":"<p>Atmospheric near surface wind speed and wind direction play an important role in many applications, ranging from air quality modeling, building design, wind turbine placement to climate change research. It is therefore crucial to accurately estimate the joint probability distribution of wind speed and direction. In this work, we develop a conditional approach to model these two variables, where the joint distribution is decomposed into the product of the marginal distribution of wind direction and the conditional distribution of wind speed given wind direction. To accommodate the circular nature of wind direction, a von Mises mixture model is used; the conditional wind speed distribution is modeled as a directional dependent Weibull distribution via a two-stage estimation procedure, consisting of a directional binned Weibull parameter estimation, followed by a harmonic regression to estimate the dependence of the Weibull parameters on wind direction. A Monte Carlo simulation study indicates that our method outperforms two other approaches in estimation efficiency: one that utilizes periodic spline quantile regression and another that generates data from the commonly used Abe-Ley distribution for cylindrical data. We illustrate our method by using the output from a regional climate model to investigate how the joint distribution of wind speed and direction may change under some future climate scenarios. Our method indicates significant changes in the variation of wind speed with respect to some directions.</p>","PeriodicalId":50512,"journal":{"name":"Environmetrics","volume":"36 3","pages":""},"PeriodicalIF":1.5,"publicationDate":"2025-03-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/env.70011","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143689690","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"环境科学与生态学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Carbon Tax Versus Renewable Energy Innovation: Theoretical Insights and Empirical Evidence 碳税与可再生能源创新:理论洞察与实证证据
IF 1.5 3区 环境科学与生态学
Environmetrics Pub Date : 2025-03-23 DOI: 10.1002/env.70010
Amit Roy, Pu Chen, Willi Semmler
{"title":"Carbon Tax Versus Renewable Energy Innovation: Theoretical Insights and Empirical Evidence","authors":"Amit Roy,&nbsp;Pu Chen,&nbsp;Willi Semmler","doi":"10.1002/env.70010","DOIUrl":"https://doi.org/10.1002/env.70010","url":null,"abstract":"<div>\u0000 \u0000 <p>In European countries, carbon pricing is often viewed as a primary strategy to combat climate change and climate risks by reducing carbon emissions and driving investment into cleaner energy sources. Decarbonization has also been suggested by directed technical change, which implements innovative renewable energy technology. We study the effectiveness of both policies for selected Northern EU countries. In a model-based investigation, we first compare optimizing and behavioral drivers of decarbonization with a focus on the two decarbonization policies. Econometrically we use local projection and the VAR method to explore the effects of both policies, carbon tax and directed technical change on GDP and emission reduction. Our results show that—although both policies are needed–significant technology-oriented policy actions on the supply side of renewable energy appear to be required to accelerate the decarbonization of the economies.</p>\u0000 </div>","PeriodicalId":50512,"journal":{"name":"Environmetrics","volume":"36 3","pages":""},"PeriodicalIF":1.5,"publicationDate":"2025-03-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143689688","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"环境科学与生态学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Correction to “Assessing Predictability of Environmental Time Series With Statistical and Machine Learning Models” 更正“用统计和机器学习模型评估环境时间序列的可预测性”
IF 1.5 3区 环境科学与生态学
Environmetrics Pub Date : 2025-02-27 DOI: 10.1002/env.70008
{"title":"Correction to “Assessing Predictability of Environmental Time Series With Statistical and Machine Learning Models”","authors":"","doi":"10.1002/env.70008","DOIUrl":"https://doi.org/10.1002/env.70008","url":null,"abstract":"<p>\u0000 <span>Newlands, N.K.</span> and <span>Lyubchich, V.</span> <span>2025</span>. “ <span>Assessing Predictability of Environmental Time Series With Statistical and Machine Learning Models</span>.” <i>Environmetrics</i> <span>36</span>(<span>2</span>), e70000. https://doi.org/10.1002/env.70000.</p><p>In the initial published version of this article, the title was incorrect. Below is the corrected article title:</p><p><b>Discussion on “Assessing Predictability of Environmental Time Series With Statistical and Machine Learning Models”</b></p><p>We apologize for this error.</p>","PeriodicalId":50512,"journal":{"name":"Environmetrics","volume":"36 2","pages":""},"PeriodicalIF":1.5,"publicationDate":"2025-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/env.70008","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143497196","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"环境科学与生态学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
New Parametric Approach for Modeling Hydrological Data: An Alternative to the Beta, Kumaraswamy, and Simplex Models 水文数据建模的新参数方法:贝塔、库马拉斯瓦米和简约模型的替代方法
IF 1.5 3区 环境科学与生态学
Environmetrics Pub Date : 2025-02-26 DOI: 10.1002/env.70006
Thiago A. N. De Andrade, Frank Gomes-Silva, Indranil Ghosh
{"title":"New Parametric Approach for Modeling Hydrological Data: An Alternative to the Beta, Kumaraswamy, and Simplex Models","authors":"Thiago A. N. De Andrade,&nbsp;Frank Gomes-Silva,&nbsp;Indranil Ghosh","doi":"10.1002/env.70006","DOIUrl":"https://doi.org/10.1002/env.70006","url":null,"abstract":"<div>\u0000 \u0000 <p>We propose a new approach of continuous distributions in the unit interval, focusing on hydrological applications. This study presents the innovative two-parameter model called <i>modified exponentiated generalized</i> (MEG) distribution. The efficiency of the MEG distribution is evidenced through its application to 29 real datasets representing the percentage of useful water volume in hydroelectric power plant reservoirs in Brazil. The model outperforms the beta, simplex, and Kumaraswamy (KW) distributions, which are widely used for this type of analysis. The connection of our proposal with classical distributions, such as the Fréchet and KW distribution, broadens its applicability. While the Fréchet distribution is recognized for its usefulness in modeling extreme values, the proximity to KW allows a comprehensive analysis of hydrological data. The simple and tractable analytical expressions of the MEG's density and cumulative and quantile functions make it computationally feasible and particularly attractive for practical applications. Furthermore, this work highlights the relevance of the related reflected model: the <i>reflected modified exponentiated generalized distribution</i>. This contribution is expected to improve the statistical modeling of hydrological phenomena and provide new perspectives for future scientific investigations.</p>\u0000 </div>","PeriodicalId":50512,"journal":{"name":"Environmetrics","volume":"36 2","pages":""},"PeriodicalIF":1.5,"publicationDate":"2025-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143489971","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"环境科学与生态学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The Effect of the North Atlantic Oscillation on Monthly Precipitation in Selected European Locations: A Non-Linear Time Series Approach 北大西洋涛动对欧洲部分地区月降水的影响:非线性时间序列方法
IF 1.5 3区 环境科学与生态学
Environmetrics Pub Date : 2025-02-24 DOI: 10.1002/env.2896
Changli He, Jian Kang, Annastiina Silvennoinen, Timo Teräsvirta
{"title":"The Effect of the North Atlantic Oscillation on Monthly Precipitation in Selected European Locations: A Non-Linear Time Series Approach","authors":"Changli He,&nbsp;Jian Kang,&nbsp;Annastiina Silvennoinen,&nbsp;Timo Teräsvirta","doi":"10.1002/env.2896","DOIUrl":"https://doi.org/10.1002/env.2896","url":null,"abstract":"<p>In this article, the relationship between the monthly precipitation in 30 European cities and towns, and two Algerian ones, and the North Atlantic Oscillation (NAO) index is characterized using the Vector Seasonal Shifting Mean and Covariance Autoregressive model, extended to contain exogenous variables. The results, based on monthly time series from 1851 up until 2020, include shifting monthly means for the rainfall series and the estimated coefficients of the exogenous NAO variable. They suggest that in the north and the west, the amount of rain in the boreal winter months has increased or stayed the same during the observation period, whereas in the Mediterranean area, there have been systematic decreases. Results on the North Atlantic Oscillation indicate that the NAO has its strongest effect on precipitation during the winter months. The (negative) effect is particularly strong in Western Europe, Lisbon, and the Mediterranean rim. In contrast, the effect in northern locations is positive for the winter months. The constancy of error variances and correlations is tested and, if rejected, the time-varying alternative is estimated. A spatial relationship between the error correlations and the distance between the corresponding pairs of cities is estimated.</p>","PeriodicalId":50512,"journal":{"name":"Environmetrics","volume":"36 2","pages":""},"PeriodicalIF":1.5,"publicationDate":"2025-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/env.2896","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143481500","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"环境科学与生态学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Discussion on Assessing Predictability of Environmental Time Series With Statistical and Machine Learning Models 用统计和机器学习模型评估环境时间序列的可预测性的讨论
IF 1.5 3区 环境科学与生态学
Environmetrics Pub Date : 2025-02-24 DOI: 10.1002/env.70003
Ansgar Steland
{"title":"Discussion on Assessing Predictability of Environmental Time Series With Statistical and Machine Learning Models","authors":"Ansgar Steland","doi":"10.1002/env.70003","DOIUrl":"https://doi.org/10.1002/env.70003","url":null,"abstract":"&lt;p&gt;I congratulate the authors for their interesting and insightful paper. Their findings contribute to the ongoing discussion of the pros and cons of machine learning methods and statistical approaches in environmetrics. In my discussion, I want to address some issues in the design of the comparison study and the interpretation of the results, and add some general thoughts. Moreover, I report about my own analyses of the Indiana citizen science data set used by the authors. Specifically, I developed a non-linear ARIMA regression model with improved heteroscedasticity-consistent uncertainty estimation, which turns out to substantially outperform the best method of (Bonas et al. &lt;span&gt;2025&lt;/span&gt;). I also applied a couple of machine learning approaches not examined there, which I regard as quite accessible general purpose machine learning methods. One of those methods is recommended by the early 2025 state-of-the-art AI large language models. I report about the interesting results in the last section.&lt;/p&gt;&lt;p&gt;The authors argue that for non-linear and non-stationary processes, machine learning methods are typically superior due to their non-parametric structure. But here one should recall that the classical but still popular class of feedforward artificial neural networks trained by backpropagation is non-linear least squares regression with a certain non-linear regression function known up to a parameter vector. In its entirety, this was mainly recognized and elaborated by the econometrician Halbert White, see White (&lt;span&gt;1992&lt;/span&gt;). And, of course, there are many methods classified as traditional statistical approaches which are non-parametric as well. The differences are more with respect to the dimensionality and sample size, and how the methods deal with it. Many machine learning methods such as artificial neural networks fit high-dimensional overparametrized parametric models, whereas statistical methods usually work with specifically chosen stochastic models aiming at parsimony. Such ML methods process high-dimensional inputs as given, and the purpose of the first stage of a model is to learn features from the input data, sometimes being agnostic with respect to the type and meaning of the input variables. The guiding principle is that one only fixes the basic topology (e.g., fully-connected layers or convolutional layers), and the model can extract optimal features provided the learning sample is large enough. This is in contrast to statistical approaches, which tend to design a model for specific types of inputs and deal with high dimensionality by suitable preprocessing steps, human-controlled feature generation and/or specific assumptions and related estimation methods, especially sparse models and sparse estimation, which combine estimation and variable selection. A further distinction is that statistical models and modeling using stochastic processes often impose a certain structure, which is derived from domain knowledge (e.g., physic","PeriodicalId":50512,"journal":{"name":"Environmetrics","volume":"36 2","pages":""},"PeriodicalIF":1.5,"publicationDate":"2025-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/env.70003","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143475634","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"环境科学与生态学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Semiparametric Copula-Based Confidence Intervals on Level Curves for the Evaluation of the Risk Level Associated to Bivariate Events 基于半参数copula的水平曲线置信区间评价与双变量事件相关的风险水平
IF 1.5 3区 环境科学与生态学
Environmetrics Pub Date : 2025-02-20 DOI: 10.1002/env.70005
Albert Folcher, Jean-François Quessy
{"title":"Semiparametric Copula-Based Confidence Intervals on Level Curves for the Evaluation of the Risk Level Associated to Bivariate Events","authors":"Albert Folcher,&nbsp;Jean-François Quessy","doi":"10.1002/env.70005","DOIUrl":"https://doi.org/10.1002/env.70005","url":null,"abstract":"&lt;p&gt;If &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;X&lt;/mi&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;mi&gt;Y&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$ left(X,Yright) $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; is a random pair with distribution function &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;F&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;X&lt;/mi&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;mi&gt;Y&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;x&lt;/mi&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;mi&gt;y&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;mo&gt;=&lt;/mo&gt;\u0000 &lt;mi&gt;ℙ&lt;/mi&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;X&lt;/mi&gt;\u0000 &lt;mo&gt;≤&lt;/mo&gt;\u0000 &lt;mi&gt;x&lt;/mi&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;mi&gt;Y&lt;/mi&gt;\u0000 &lt;mo&gt;≤&lt;/mo&gt;\u0000 &lt;mi&gt;y&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$ {F}_{X,Y}left(x,yright)=mathbb{P}left(Xle x,Yle yright) $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, one can define the level curve of probability &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;p&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$ p $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; as the values of &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;x&lt;/mi&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;mi&gt;y&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;mo&gt;∈&lt;/mo&gt;\u0000 &lt;msup&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;ℝ&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msup&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$ left(x,yright)in {mathbb{R}}^2 $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; such that &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;F&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;X&lt;/mi&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;mi&gt;Y&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;x&lt;/mi&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;mi&gt;y&lt;/mi&gt;\u0000 ","PeriodicalId":50512,"journal":{"name":"Environmetrics","volume":"36 2","pages":""},"PeriodicalIF":1.5,"publicationDate":"2025-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/env.70005","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143456021","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"环境科学与生态学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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