Fitting real data by means of non-homogeneous log-normal diffusion processes

Abstract Urban mobility data are important to areas ranging from traffic engineering to the analysis of outbreaks and disasters. In this paper, we study mobility data from a major Brazilian city from a geographical viewpoint using a Complex Network approach. The case study is based on intra-urban mobility data from the Metropolitan area of Rio de Janeiro (Brazil), presenting more than 480 spatial network nodes. While for the mobility flow data a log-normal distribution outperformed the power law, we also found moderate evidence for scale-free and small word effects in the flow network’s degree distribution. We employ a novel open-source GIS tool to display (geo)graph’s topological properties in maps and observe a strong traffic-topology association and also a fine adjustment for hubs location for different flow threshold networks. In the central commercial area for lower thresholds and in high population residential areas for higher thresholds. This set of results, including statistical, topological and geographical analysis may represent an important tool for policymakers and stakeholders in the urban planning area, especially by the identification of zones with few but strong links in a real data-driven mobility network.

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On the quasi-Monte Carlo method with Halton points for elliptic PDEs with log-normal diffusion

Mathematics of Computation ◽

10.1090/mcom/3107 ◽

2016 ◽

Vol 86 (304) ◽

pp. 771-797 ◽

Cited By ~ 9

Author(s):

Helmut Harbrecht ◽

Michael Peters ◽

Markus Siebenmorgen

Keyword(s):

Monte Carlo ◽

Monte Carlo Method ◽

Elliptic Pdes ◽

Quasi Monte Carlo ◽

Normal Diffusion ◽

Log Normal

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A New Extended-X Family of Distributions: Properties and Applications

Computational and Mathematical Methods in Medicine ◽

10.1155/2020/4650520 ◽

2020 ◽

Vol 2020 ◽

pp. 1-13

Author(s):

Mi Zichuan ◽

Saddam Hussain ◽

Anum Iftikhar ◽

Muhammad Ilyas ◽

Zubair Ahmad ◽

...

Keyword(s):

Real Data ◽

Model Parameters ◽

Data Sets ◽

Statistical Distributions ◽

Reliability Engineering ◽

Monte Carlo Simulation Study ◽

Diverse Range ◽

Heavy Tailed ◽

Log Normal ◽

Extended Weibull Distribution

During the past couple of years, statistical distributions have been widely used in applied areas such as reliability engineering, medical, and financial sciences. In this context, we come across a diverse range of statistical distributions for modeling heavy tailed data sets. Well-known distributions are log-normal, log-t, various versions of Pareto, log-logistic, Weibull, gamma, exponential, Rayleigh and its variants, and generalized beta of the second kind distributions, among others. In this paper, we try to supplement the distribution theory literature by incorporating a new model, called a new extended Weibull distribution. The proposed distribution is very flexible and exhibits desirable properties. Maximum likelihood estimators of the model parameters are obtained, and a Monte Carlo simulation study is conducted to assess the behavior of these estimators. Finally, we provide a comparative study of the newly proposed and some other existing methods via analyzing three real data sets from different disciplines such as reliability engineering, medical, and financial sciences. It has been observed that the proposed method outclasses well-known distributions on the basis of model selection criteria.

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The Odd Log-Logistic Log-Normal Distribution with Theory and Applications

Advances in Data Science and Adaptive Analysis ◽

10.1142/s2424922x18500092 ◽

2018 ◽

Vol 10 (04) ◽

pp. 1850009 ◽

Cited By ~ 1

Author(s):

Gamze Ozel ◽

Emrah Altun ◽

Morad Alizadeh ◽

Mahdieh Mozafari

Keyword(s):

Normal Distribution ◽

Likelihood Estimation ◽

Real Data ◽

Estimation Procedure ◽

Quantile Function ◽

Logistic Distribution ◽

Unknown Parameters ◽

Heavy Tailed ◽

Log Normal ◽

Log Normal Distribution

In this paper, a new heavy-tailed distribution is used to model data with a strong right tail, as often occuring in practical situations. The proposed distribution is derived from the log-normal distribution, by using odd log-logistic distribution. Statistical properties of this distribution, including hazard function, moments, quantile function, and asymptotics, are derived. The unknown parameters are estimated by the maximum likelihood estimation procedure. For different parameter settings and sample sizes, a simulation study is performed and the performance of the new distribution is compared to beta log-normal. The new lifetime model can be very useful and its superiority is illustrated by means of two real data sets.

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Modeling stochastic processes in disease spread across a heterogeneous social system

Proceedings of the National Academy of Sciences ◽

10.1073/pnas.1801429116 ◽

2018 ◽

Vol 116 (2) ◽

pp. 401-406 ◽

Cited By ~ 6

Author(s):

Minkyoung Kim ◽

Dean Paini ◽

Raja Jurdak

Keyword(s):

Stochastic Processes ◽

Social System ◽

Diffusion Processes ◽

Human Mobility ◽

Real Data ◽

Cost Effective ◽

Human Case ◽

Disease Spread ◽

Effective Control ◽

Diffusion Dynamics

Diffusion processes are governed by external triggers and internal dynamics in complex systems. Timely and cost-effective control of infectious disease spread critically relies on uncovering underlying diffusion mechanisms, which is challenging due to invisible infection pathways and time-evolving intensity of infection cases. Here, we propose a new diffusion framework for stochastic processes, which models disease spread across metapopulations by incorporating human mobility as topological pathways in a heterogeneous social system. We apply Bayesian inference with the stochastic Expectation–Maximization algorithm to quantify underlying diffusion dynamics in terms of exogeneity and endogeneity and estimate cross-regional infection flow based on Granger causality. The effectiveness of our proposed model is shown by using comprehensive simulation procedures (robustness tests with noisy data considering missing or delayed human case reporting in real situations) and by applying the model to real data from 15-y dengue outbreaks in Australia.

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Optimal consumption/portfolio choice with borrowing rate higher than deposit rate

The Journal of the Australian Mathematical Society Series B Applied Mathematics ◽

10.1017/s0334270000007748 ◽

1998 ◽

Vol 39 (4) ◽

pp. 449-462 ◽

Cited By ~ 2

Author(s):

Wensheng Xu ◽

Shuping Chen

Keyword(s):

Portfolio Choice ◽

Optimal Strategies ◽

Optimal Investment ◽

Dynamic Programming Principle ◽

Optimal Consumption ◽

Bank Account ◽

Normal Diffusion ◽

Hamilton Jacobi Bellman ◽

Log Normal ◽

Optimal Consumption And Investment

AbstractIn this paper, optimal consumption and investment decisions are studied for an investor who has available a bank account and a stock whose price is a log normal diffusion. The bank pays at an interest rate r(t) for any deposit, and vice takes at a larger rate r′(t) for any loan. Optimal strategies are obtained via Hamilton-Jacobi-Bellman (HJB) equation which is derived from dynamic programming principle. For the specific HARA case, we get the optimal consumption and optimal investment explicitly, which coincides with the classical one under the condition r′(t) ≡ r(t)

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Two symmetric and computationally efficient Gini correlations

Dependence Modeling ◽

10.1515/demo-2020-0020 ◽

2020 ◽

Vol 8 (1) ◽

pp. 373-395

Author(s):

Courtney Vanderford ◽

Yongli Sang ◽

Xin Dang

Keyword(s):

Influence Function ◽

Random Variables ◽

Real Data ◽

Computationally Efficient ◽

Gini Correlation ◽

Heavy Tailed Distributions ◽

Data Application ◽

Heavy Tailed ◽

Log Normal ◽

Log Normal Distribution

AbstractStandard Gini correlation plays an important role in measuring the dependence between random variables with heavy-tailed distributions. It is based on the covariance between one variable and the rank of the other. Hence for each pair of random variables, there are two Gini correlations and they are not equal in general, which brings a substantial difficulty in interpretation. Recently, Sang et al (2016) proposed a symmetric Gini correlation based on the joint spatial rank function with a computation cost of O(n2) where n is the sample size. In this paper, we study two symmetric and computationally efficient Gini correlations with the computational complexity of O(n log n). The properties of the new symmetric Gini correlations are explored. The influence function approach is utilized to study the robustness and the asymptotic behavior of these correlations. The asymptotic relative efficiencies are considered to compare several popular correlations under symmetric distributions with different tail-heaviness as well as an asymmetric log-normal distribution. Simulation and real data application are conducted to demonstrate the desirable performance of the two new symmetric Gini correlations.

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Random intercept and linear mixed models including heteroscedasticity in a logarithmic scale: Correction terms and prediction in the original scale

PLoS ONE ◽

10.1371/journal.pone.0249910 ◽

2021 ◽

Vol 16 (4) ◽

pp. e0249910

Author(s):

Ricardo Ramírez-Aldana ◽

Lizbeth Naranjo

Keyword(s):

Mixed Models ◽

Linear Mixed Models ◽

Real Data ◽

Logarithmic Scale ◽

Response Variable ◽

Random Intercept ◽

Original Scale ◽

Log Normal ◽

Correction Terms ◽

Log Normal Distribution

Random intercept models are linear mixed models (LMM) including error and intercept random effects. Sometimes heteroscedasticity is included and the response variable is transformed into a logarithmic scale, while inference is required in the original scale; thus, the response variable has a log-normal distribution. Hence, correction terms should be included to predict the response in the original scale. These terms multiply the exponentiated predicted response variable, which subestimates the real values. We derive the correction terms, simulations and real data about the income of elderly are presented to show the importance of using them to obtain more accurate predictions. Generalizations for any LMM are also presented.

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