American journal of applied mathematics and statistics最新文献_第5页

Prediction of Precipitation Rate Based on Stationary Extreme Value Theory 基于平稳极值理论的降水率预测

American journal of applied mathematics and statistics Pub Date : 2021-10-30 DOI: 10.11648/J.AJAM.20210905.13

J. Han

{"title":"Prediction of Precipitation Rate Based on Stationary Extreme Value Theory","authors":"J. Han","doi":"10.11648/J.AJAM.20210905.13","DOIUrl":"https://doi.org/10.11648/J.AJAM.20210905.13","url":null,"abstract":"For the determination of the effectiveness of weather forecasts such as temperature or flooding forecast, the single variable linear regression or simple exponential smoothing will not be an effective way. To accurately predict the effectiveness of such a trend, iterative and statistical methods that can determine the status of temperature or flooding in the United States were chosen in this paper. The task of modeling the pattern in a focused period and performing data analysis was performed. For the analysis, the extreme value theory was used to assess extreme events within probability distributions by quantifying tail behavior. The python tools are utilized for the analysis of big data. By analyzing the maximum values of samples, it was possible to determine probabilities for extreme events. A comparison was made with events previously observed and analyzed for authenticity. As evident in our observations, lower values of data have much shorter return periods. In other words, they are more likely to reoccur; however, as the values increase for higher precipitation values, the length of the return periods increase exponentially. Therefore, there is a tendency for precipitation values to remain in lower ranges. In this paper, the USGS geographical information and Gumbel distribution were used to find the return period corresponding to the exceedance probability. The Gumbel distribution is applied to Allegheny River, New York and Whetstone River, San Diego.","PeriodicalId":91196,"journal":{"name":"American journal of applied mathematics and statistics","volume":"115 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77693914","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 1

Solution to Collatz Conjecture Collatz猜想的解

American journal of applied mathematics and statistics Pub Date : 2021-10-12 DOI: 10.12691/AJAMS-9-3-5

Abhijit Manohar

引用次数: 0

On Evaluating the Volatility of Nigerian Gross Domestic Product Using Smooth Transition Autoregressive-GARCH (STAR - GARCH) Models 用平滑过渡自回归GARCH (STAR -GARCH)模型评估尼日利亚国内生产总值的波动性

American journal of applied mathematics and statistics Pub Date : 2021-10-11 DOI: 10.12691/AJAMS-9-3-4

Akintunde Mutairu Oyewale

{"title":"On Evaluating the Volatility of Nigerian Gross Domestic Product Using Smooth Transition Autoregressive-GARCH (STAR - GARCH) Models","authors":"Akintunde Mutairu Oyewale","doi":"10.12691/AJAMS-9-3-4","DOIUrl":"https://doi.org/10.12691/AJAMS-9-3-4","url":null,"abstract":"STAR-GARCH models are hybrid models that combine the functional form of smooth transition autoregressive models and Generalized autoregressive conditional heteroscedasticity models. The two classes of STAR models considered in this paper are Exponential and Logistic Smooth transition autoregressive models (ESTAR and LSTAR). The functional form of each of this was combined with that of GARCH model and the resulting models becomes ESTAR-GARCH and LSTAR-GARCH models. The derived equations were applied to Nigerian gross domestic product (Real estate) for empirical illustration. Statonarity tests (Unit root test Graphical and correlogrom methods) conducted revealed that the series was stationary at Second difference. The hybrid models equations so derived were used to determine the model that performed better using the information criteria (AIC, SIC and HQIC), variances obtained from the data, performance measure indices (RMSE, MAE, MAPE THEIL U, Bias proportion, variance Bias proportion and covariance Bias proportion) analysis and in - sample forecast accuracy for the models. From all the criteria used it was observed that the duo of LSTAR-GARCH and ESTAR-GARCH models performed far better than classical GARCH model. However, LSTAR-GARCH performs slightly better than ESTAR-GARCH. From these results it is evident that volatility in Nigerian gross domestic product (Real estate) is best captured using Logistic smooth transition GARCH (LSTAR-GARCH) models, it is therefore, recommended for would be forecasters, investors and other end users to make use of LSTAR-GARCH models.","PeriodicalId":91196,"journal":{"name":"American journal of applied mathematics and statistics","volume":"12 8","pages":"102-106"},"PeriodicalIF":0.0,"publicationDate":"2021-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72461767","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Normal-Power Function Distribution with Logistic Quantile Function: Properties and Application Logistic分位数函数的正态幂函数分布:性质及应用

American journal of applied mathematics and statistics Pub Date : 2021-09-17 DOI: 10.12691/AJAMS-9-3-3

M. Ekum, O. Job, Jimoh Taylor, Asimi A. Amalare, M. A. Khaleel, A. S. Ogunsanya

{"title":"Normal-Power Function Distribution with Logistic Quantile Function: Properties and Application","authors":"M. Ekum, O. Job, Jimoh Taylor, Asimi A. Amalare, M. A. Khaleel, A. S. Ogunsanya","doi":"10.12691/AJAMS-9-3-3","DOIUrl":"https://doi.org/10.12691/AJAMS-9-3-3","url":null,"abstract":"Developing compound probability distributions is very important in the field of probability and statistics because there are different datasets from different fields with different features. These features range from high skewness, peakedness (kurtosis), bimodality, highly dispersed, and so on. Existing distributions might not easily fit well to these emerging data of interest. So, there is a need to develop more robust and flexible distributions that are positively skewed, negatively skewed, and bathup shape, to handle some of these features in the emerging data of interest. This paper, therefore, proposed a new four-parameter distribution called the Normal-Power{logistic} distribution. The proposed distribution was characterized by its density, distribution, survival, hazard, cumulative hazard, reversed hazard, and quantile functions. Properties such as the r-th moment, heavy tail property, stochastic ordering, mean inactive time were obtained. A useful transformation of the proposed distribution to normal distribution was shown to help generate its quantiles. The method of Maximum Likelihood Estimation (MLE) was used to estimate the model parameters. A simulation study was carried out to test the consistency of the maximum likelihood parameter estimates. The result of the simulation shows that the biases reduce as the sample size increases for different parameter values. The importance of the new distribution was proved empirically using a real-life dataset of gauge lengths of 10mm. The proposed distribution was compared with five other competing distributions, and the results show that the proposed Normal-Power{logistic} distribution (NPLD) performed favourably than the other five distributions using the AIC, CAIC, BIC, HQIC criteria.","PeriodicalId":91196,"journal":{"name":"American journal of applied mathematics and statistics","volume":"22 1","pages":"90-101"},"PeriodicalIF":0.0,"publicationDate":"2021-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84849357","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 3

Proportional Subdistribution Hazards Model for Competing Risks in Case-Cohort Studies 病例队列研究中竞争风险的比例亚分布风险模型

American journal of applied mathematics and statistics Pub Date : 2021-09-09 DOI: 10.11648/J.AJAM.20210905.12

A. Wogu, Shanshan Zhao, H. Nichols, Jianwen Cai

{"title":"Proportional Subdistribution Hazards Model for Competing Risks in Case-Cohort Studies","authors":"A. Wogu, Shanshan Zhao, H. Nichols, Jianwen Cai","doi":"10.11648/J.AJAM.20210905.12","DOIUrl":"https://doi.org/10.11648/J.AJAM.20210905.12","url":null,"abstract":"Competing risks refer to the situation where there are multiple causes of failure and the occurrence of one type of event prohibits the occurrence of the other types of event or alters the chance to observe them. In large cohort studies with long-term follow-up, there are often competing risks. When the failure events are rare, or the information on certain risk factors is difficult or costly to measure for the full cohort, a case-cohort study design can be a desirable approach. In this paper, we consider a semiparametric proportional subdistribution hazards model in the presence of competing risks in case-cohort studies. The subdistribution hazards function, unlike the cause-specific hazards function, gives the advantage of outlining the marginal probability of a particular type of event. We propose estimating equations based on inverse probability weighting techniques for the estimation of the model parameters. In the estimation methods, we considered a weighted availability indicator to properly account for the case-cohort sampling scheme. We also proposed a Breslow-type estimator for the cumulative baseline subdistribution hazard function. The resulting estimators are shown, using empirical processes and martingale properties, to be consistent and asymptotically normally distributed. The performance of the proposed methods in finite samples are examined through simulation studies by considering different levels of censoring and event of interest percentages. The simulation results from the different scenarios suggest that the parameter estimates are reasonably close to the true values of the respective parameters in the model. Finally, the proposed estimation methods are applied to a case-cohort sample from the Sister Study, in which we illustrated the proposed methods by studying the association between selected CpGs and invasive breast cancer in the presence of ductal carcinoma in situ as competing risk.","PeriodicalId":91196,"journal":{"name":"American journal of applied mathematics and statistics","volume":"12 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91213995","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Method of Construction of the Stochastic Integral with Respect to Fractional Brownian Motion 分数阶布朗运动随机积分的构造方法

American journal of applied mathematics and statistics Pub Date : 2021-09-03 DOI: 10.11648/J.AJAM.20210905.11

D. Bou, Ba Demba Bocar, Thioune Moussa

{"title":"Method of Construction of the Stochastic Integral with Respect to Fractional Brownian Motion","authors":"D. Bou, Ba Demba Bocar, Thioune Moussa","doi":"10.11648/J.AJAM.20210905.11","DOIUrl":"https://doi.org/10.11648/J.AJAM.20210905.11","url":null,"abstract":"Since the pioneering work of Hurst, and Mandelbrot, the fractional brownian motions have played and increasingly important role in many fields of application such as hydrology, economics and telecommunications. For every value of the Hurst index H ∈ (0,1) we define a stochastic integral with respect to fractional Brownian motion of index H. This process is called a (standard) fractional Brownian motion with Hurst parameter H. To simplify the presentation, it is always assumed that the fractional Brownian motion is 0 at t=0. If H = 1/2, then the corresponding fractional Brownian motion is the usual standard Brownian motion. If 1/2 < H < 1, Fractional Brownian motion (FBM) is neither a finite variation nor a semi-martingale. Consequently, the standard Ito calculus is not available for stochastic integrals with respect to FBM as an integrator if 1/2 < H < 1. The classic methods (Ito and Stiliege) are excluted. The most studied case is that where H is between 0 and 1/2. Several attempts to define the stochastic integral are made. But so far some difficulties subjust. We give in this paper, several construction methods. So for the construction, we will use other tools to deal with such situations.","PeriodicalId":91196,"journal":{"name":"American journal of applied mathematics and statistics","volume":"11 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82591732","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

The Orthogonality of Two-scale Three-dimensional Eight-direction Wavelet 二尺度三维八向小波的正交性

American journal of applied mathematics and statistics Pub Date : 2021-08-31 DOI: 10.11648/j.ajam.20210904.15

Jing Zhang, Gang Wang, Chuanyan Hou, Xiaoying Yang

引用次数: 0

Assessing Implicit Causes of Fast-Food Demand Fluctuation Through Facilitating an Exploratory Factor Analysis 通过促进探索性因素分析来评估快餐需求波动的隐性原因

American journal of applied mathematics and statistics Pub Date : 2021-08-04 DOI: 10.12691/ajams-9-3-2

M. Uddin, Golam Sakaline, Sahla Nawal Meem, Runumi Das

引用次数: 1

Modelling Forest Growth Indices on Vegetation Pattern Formation 基于植被格局形成的森林生长指数模拟

American journal of applied mathematics and statistics Pub Date : 2021-08-02 DOI: 10.11648/J.AJAM.20210904.13

P. Nyarko, C. Nyarko

{"title":"Modelling Forest Growth Indices on Vegetation Pattern Formation","authors":"P. Nyarko, C. Nyarko","doi":"10.11648/J.AJAM.20210904.13","DOIUrl":"https://doi.org/10.11648/J.AJAM.20210904.13","url":null,"abstract":"Forest dynamics is mostly concerned with the changes in forest structure and composition over time, including its behavior in response to anthropogenic and natural destructions which is one of the primary evidence of forest change. This study presents the dynamics of vegetation pattern formation taken into account all the interaction measure indices such as light, water, temperature and nutrients fertility. Michaelis-Menten Kinetics and a Continuous-Time Markov (CTM) method were employed to determine plant metabolism responses to all the inputs. The Continuous-Time Markov (CTM) technique was then used to obtain a simple plant growth component by synthesizing the four - measure indices or resources (light, water and nutrients and temperature). Stability analysis of the formulated model was carried out to determine the possible phase regions associated with the various stability states for a sufficiently precise representation of the essential features of the model. Results of the β values for the spatial patterns obtained indicate association or interaction among the various soil fertility levels under different water conditions. For instance, a β value of 0.05605 represents control fertility under arid conditions, indicates a vegetation pattern with numerous and wider patches of bare or almost bare land compared to patterns exhibited by the other fertility levels.","PeriodicalId":91196,"journal":{"name":"American journal of applied mathematics and statistics","volume":"210 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-08-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76122826","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

On the Unique Solvability of the Generalized Absolute Value Matrix Equation 广义绝对值矩阵方程的唯一可解性

American journal of applied mathematics and statistics Pub Date : 2021-08-02 DOI: 10.11648/j.ajam.20210904.12

K. Xie

引用次数: 5