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Secretary problem and two almost the same consecutive applicants 秘书问题和两个几乎相同的连续申请者
Mathematica Applicanda Pub Date : 2021-06-21 DOI: 10.14708/ma.v50i2.7143
Josef Rukavicka
{"title":"Secretary problem and two almost the same consecutive applicants","authors":"Josef Rukavicka","doi":"10.14708/ma.v50i2.7143","DOIUrl":"https://doi.org/10.14708/ma.v50i2.7143","url":null,"abstract":"We present a new variant of the secretary problem. Let $A$ be a totally ordered set of $n$ emph{applicants}. Given $Psubseteq A$ and $xin A$, let $rr(P,x)=vert{zin P mid zleq x}vertmbox{ }$ be the emph{relative rank of} $x$ emph{with regard to} $P$, and let $rr_n(x)=rr(A,x)$. Let $x_1,x_2,dots,x_nin A$ be a random sequence of distinct applicants. The aim is to select $1<jleq n$ such that $rr_n(x_{j-1})-rr_n(x_j)in{-1,1}$. Let $alpha$ be a real constant with $0<alpha<1$. Suppose the following stopping rule $tau_n(alpha)$: reject first $alpha n$ applicants and then select the first $x_j$ such that $rr(P_j,x_{j-1})-rr(P_j,x_j)in{-1,1}$, where $P_j={x_imid 1leq ileq j}$. Let $p_{n,tau}(alpha)$ be the probability that $tau_n(alpha)$ selects $x_j$ such that $rr_n(x_{j-1})-rr_n(x_j)in{-1,1}$. We show that [lim_{nrightarrowinfty}p_{n,tau}(alpha)leq lim_{nrightarrowinfty}p_{n,tau}left(frac{1}{2}right)=frac{1}{2}mbox{.}]","PeriodicalId":36622,"journal":{"name":"Mathematica Applicanda","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48780419","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
Chance constraint programming problems with parameters as exponential random variable 参数为指数型随机变量的机会约束规划问题
Mathematica Applicanda Pub Date : 2021-06-20 DOI: 10.14708/MA.V49I1.7051
V. Sarkar
{"title":"Chance constraint programming problems with parameters as exponential random variable","authors":"V. Sarkar","doi":"10.14708/MA.V49I1.7051","DOIUrl":"https://doi.org/10.14708/MA.V49I1.7051","url":null,"abstract":"Robust decision making under uncertainty is deemed to be a crucial factor in many discipline and application areas. Also management and measurement of risk is an important issue in almost all areas that require decisions to be made under uncertain information. Chance constrained programming (CCP) has been used for modelling and analysis of risks in a number of application domains. This paper \u0000presents a deterministic reduction of linear and nonlinear chance constraint programming problem using simple mathematical and statistical tools, assuming the coefficients of the decision variables in the chance constraints as exponential random variables. After converting the proposed chance constraint programming problem \u0000into a deterministic problem, standard generic package is used to find the compromise solution and also comparison with some other technique is considered. Then MATLAB programming code is used to verify the validity of solution for the original chance constraints.","PeriodicalId":36622,"journal":{"name":"Mathematica Applicanda","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48874561","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 postdoc variant of the secretary problem 秘书问题的博士后变体
Mathematica Applicanda Pub Date : 2021-06-19 DOI: 10.14708/MA.V49I1.7076
R. Vanderbei
{"title":"The postdoc variant of the secretary problem","authors":"R. Vanderbei","doi":"10.14708/MA.V49I1.7076","DOIUrl":"https://doi.org/10.14708/MA.V49I1.7076","url":null,"abstract":"The classical secretary problem involves sequentially interviewing a pool of n applicants with the aim of hiring exactly the best one in the pool—nothing less is good enough. The optimal decision strategy is easy to describe and the probability of success is 1/e. In this paper, we consider a minor variant of this classical problem. We wish to pick not the best but the second-best (the best is going to Harvard). In this case, an explicit solution can be given both for the optimal strategy and the associated optimal success probability. As n goes to infinity, the probability of success tends to 1/4. Apparently, it is easier to pick the best than the second best.","PeriodicalId":36622,"journal":{"name":"Mathematica Applicanda","volume":"49 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44792859","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: 10
Parisian ruin probability - the De Vylder type approximation 巴黎破产概率——De Vylder型近似
Mathematica Applicanda Pub Date : 2021-03-30 DOI: 10.14708/MA.V48I2.7069
M. Teuerle, Martyna Zdeb
{"title":"Parisian ruin probability - the De Vylder type approximation","authors":"M. Teuerle, Martyna Zdeb","doi":"10.14708/MA.V48I2.7069","DOIUrl":"https://doi.org/10.14708/MA.V48I2.7069","url":null,"abstract":"","PeriodicalId":36622,"journal":{"name":"Mathematica Applicanda","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49445687","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
A principal component analysis of multivariate data on inflation for Nigeria 尼日利亚通货膨胀多变量数据的主成分分析
Mathematica Applicanda Pub Date : 2021-03-30 DOI: 10.14708/MA.V48I2.7043
David E. Omoregie, V. Ekhosuehi
{"title":"A principal component analysis of multivariate data on inflation for Nigeria","authors":"David E. Omoregie, V. Ekhosuehi","doi":"10.14708/MA.V48I2.7043","DOIUrl":"https://doi.org/10.14708/MA.V48I2.7043","url":null,"abstract":"For quite some time now, the Central Bank of Nigeria (CBN) analyses multivariate data on inflation so as to account for diverse sources of inflationary pressures at the current period and to monitor the inflation pattern in the economy. When the data are subjected to the classical multiple regression analysis using the Ordinary Least Squares (OLS) method, some of the variables may be highly correlated causing statistical insignificance. This may lead to exclusion of some variables from the fitted model. When this happens, the cost of data collection for such variables is a waste. Regardless of the outcome from a variable selection technique, this study is designed to familiarise monetary policy makers with the possibility of integrating Principal Component Analysis (PCA) with regression analysis so that a few variable components are utilised without excluding any explanatory variable. The paper models the multivariate data at the CBN database on inflation, and extracts important artificial orthogonal variables from the linear combinations of the observed explanatory variables, although with a penalty cost of excluding components with observations that are minimally separated. The PC-based model explains 95.91% of variations in the headline inflation with a mean difference (between the actual and the predicted inflation) that is statistically not different from zero. The study is a significant addition to the existing methodologies for inflation forecasting in the literature as it is one of a few works that apply PCA-based technique to predict headline inflation.","PeriodicalId":36622,"journal":{"name":"Mathematica Applicanda","volume":"48 1","pages":"115-132"},"PeriodicalIF":0.0,"publicationDate":"2021-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43177780","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
Modeling of the process of technological breakdown 技术故障过程的建模
Mathematica Applicanda Pub Date : 2021-03-30 DOI: 10.14708/MA.V48I2.7070
Marek Skarupski, Radosław Markulak
{"title":"Modeling of the process of technological breakdown","authors":"Marek Skarupski, Radosław Markulak","doi":"10.14708/MA.V48I2.7070","DOIUrl":"https://doi.org/10.14708/MA.V48I2.7070","url":null,"abstract":"","PeriodicalId":36622,"journal":{"name":"Mathematica Applicanda","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49213017","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 maximum likelihood method for Student's t-distributed autoregressive model with infinite variance 无穷方差学生t分布自回归模型的极大似然法
Mathematica Applicanda Pub Date : 2021-03-30 DOI: 10.14708/MA.V48I2.7059
A. Wyłomańska, P. Stepniak
{"title":"The maximum likelihood method for Student's t-distributed autoregressive model with infinite variance","authors":"A. Wyłomańska, P. Stepniak","doi":"10.14708/MA.V48I2.7059","DOIUrl":"https://doi.org/10.14708/MA.V48I2.7059","url":null,"abstract":"","PeriodicalId":36622,"journal":{"name":"Mathematica Applicanda","volume":"48 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43802684","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
The Huber Functions and Their Application to a Classification Problem Huber函数及其在分类问题中的应用
Mathematica Applicanda Pub Date : 2021-03-30 DOI: 10.14708/MA.V48I2.7045
Agnieszka Kulawik, H. Gacki
{"title":"The Huber Functions and Their Application to a Classification Problem","authors":"Agnieszka Kulawik, H. Gacki","doi":"10.14708/MA.V48I2.7045","DOIUrl":"https://doi.org/10.14708/MA.V48I2.7045","url":null,"abstract":"","PeriodicalId":36622,"journal":{"name":"Mathematica Applicanda","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45635071","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
Bounds for expected payoff on two stocks 两支股票的预期收益界限
Mathematica Applicanda Pub Date : 2020-10-05 DOI: 10.14708/ma.v48i1.6511
C. Makasu
{"title":"Bounds for expected payoff on two stocks","authors":"C. Makasu","doi":"10.14708/ma.v48i1.6511","DOIUrl":"https://doi.org/10.14708/ma.v48i1.6511","url":null,"abstract":"","PeriodicalId":36622,"journal":{"name":"Mathematica Applicanda","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-10-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45630010","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
Nonlinear mixed effect modeling in recognition of underlying population dynamics 潜在种群动态识别中的非线性混合效应建模
Mathematica Applicanda Pub Date : 2020-10-05 DOI: 10.14708/ma.v48i1.7042
U. Foryś
{"title":"Nonlinear mixed effect modeling in recognition of underlying population dynamics","authors":"U. Foryś","doi":"10.14708/ma.v48i1.7042","DOIUrl":"https://doi.org/10.14708/ma.v48i1.7042","url":null,"abstract":"","PeriodicalId":36622,"journal":{"name":"Mathematica Applicanda","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-10-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48143240","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
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