scholarly journals Stochastic Brennan–Schwartz Diffusion Process: Statistical Computation and Application

Mathematics ◽  
2019 ◽  
Vol 7 (11) ◽  
pp. 1062 ◽  
Author(s):  
Ahmed Nafidi ◽  
Ghizlane Moutabir ◽  
Ramón Gutiérrez-Sánchez
Keyword(s):  
Diffusion Process ◽  
Real Data ◽  
Convertible Bond ◽  
Financial Mathematics ◽  
Continuous Sampling ◽  
Statistical Computation ◽  
Likelihood Approach ◽  
Lognormal Diffusion Process ◽  
Trend Functions ◽  
The One

In this paper, we study the one-dimensional homogeneous stochastic Brennan–Schwartz diffusion process. This model is a generalization of the homogeneous lognormal diffusion process. What is more, it is used in various contexts of financial mathematics, for example in deriving a numerical model for convertible bond prices. In this work, we obtain the probabilistic characteristics of the process such as the analytical expression, the trend functions (conditional and non-conditional), and the stationary distribution of the model. We also establish a methodology for the estimation of the parameters in the process: First, we estimate the drift parameters by the maximum likelihood approach, with continuous sampling. Then, we estimate the diffusion coefficient by a numerical approximation. Finally, to evaluate the capability of this process for modeling real data, we applied the stochastic Brennan–Schwartz diffusion process to study the evolution of electricity net consumption in Morocco.

scholarly journals Stochastic Diffusion Process Based on Generalized Brody Curve: Application to Real Data

2021 ◽  
Vol 2 (1) ◽  
pp. 01-11
Author(s):  
Ahmed Nafidi ◽  
Oussama Rida ◽  
Boujemaa Achchab
Keyword(s):  
Diffusion Process ◽  
Transition Density ◽  
Real Data ◽  
Parameters Estimation ◽  
Likelihood Method ◽  
Stochastic Diffusion ◽  
Life Expectancy At Birth ◽  
Transition Density Function ◽  
Lognormal Diffusion Process ◽  
Trend Functions

A new stochastic diffusion process based on Generalized Brody curve is proposed. Such a process can be considered as an extension of the nonhomogeneous lognormal diffusion process. From the corresponding Itô’s stochastic differential equation (SDE), firstly we establish the probabilistic characteristics of the studied process, such as the solution to the SDE, the probability transition density function and their distribution, the moments function, in particular the conditional and non-conditional trend functions. Secondly, we treat the parameters estimation problem by using the maximum likelihood method in basis of the discrete sampling, thus we obtain nonlinear equations that can be solved by metaheuristic optimization algorithms such as simulated annealing and variable search neighborhood. Finally, we perform a simulation studies and we apply the model to the data of life expectancy at birth in Morocco.

scholarly journals T-Growth Stochastic Model: Simulation and Inference via Metaheuristic Algorithms

Mathematics ◽  
2021 ◽  
Vol 9 (9) ◽  
pp. 959
Author(s):  
Antonio Barrera ◽  
Patricia Román-Román ◽  
Francisco Torres-Ruiz
Keyword(s):  
Stochastic Model ◽  
Diffusion Process ◽  
Model Simulation ◽  
Likelihood Estimation ◽  
Real Data ◽  
Estimation Procedure ◽  
Metaheuristic Algorithms ◽  
Mathematical Treatment ◽  
Linear Differential ◽  
Lognormal Diffusion Process

The main objective of this work is to introduce a stochastic model associated with the one described by the T-growth curve, which is in turn a modification of the logistic curve. By conveniently reformulating the T curve, it may be obtained as a solution to a linear differential equation. This greatly simplifies the mathematical treatment of the model and allows a diffusion process to be defined, which is derived from the non-homogeneous lognormal diffusion process, whose mean function is a T curve. This allows the phenomenon under study to be viewed in a dynamic way. In these pages, the distribution of the process is obtained, as are its main characteristics. The maximum likelihood estimation procedure is carried out by optimization via metaheuristic algorithms. Thanks to an exhaustive study of the curve, a strategy is obtained to bound the parametric space, which is a requirement for the application of various swarm-based metaheuristic algorithms. A simulation study is presented to show the validity of the bounding procedure and an example based on real data is provided.

scholarly journals The Stochastic Modified Lundqvist-Korf Diffusion Process: Statistical and Computational Aspects and Application to Modeling of the CO2 Emission in Morocco

2021 ◽  
Author(s):  
Ahmed Nafidi ◽  
Abdenbi El azri ◽  
Ramón Gutiérrez Sanchez
Keyword(s):  
Diffusion Process ◽  
Estimation Method ◽  
Likelihood Estimation ◽  
Real Data ◽  
Trend Function ◽  
Non Linear Equation ◽  
New Process ◽  
Computational Aspects ◽  
Exogenous Factors ◽  
Trend Functions

Abstract The main goal of this paper is to study the possibility of using a stochastic non-homogeneous (without exogenous factors) diffusion process to model the evolution of CO2 emissions in Morocco and concretely using a new process, in which the trend function is proportional to the modified Lundqvist-Korf growth curve. First, the main characteristics of the process are studied, then we establish a computational statistical methodology based on the maximum likelihood estimation method and the trend functions. When we are estimating the parameters of the process, a non-linear equation is obtained and the simulated annealing method is proposed to solve it after bounding the parametric space by a stagewise procedure. Also, to validate this methodology, we include the results obtained from several examples of simulation. Finally, the process and the methodology established are applied to real data corresponding to the evolution of CO2 emissions in Morocco.

Intuitionistic fuzzy two-factor variance analysis of movie ticket sales

2021 ◽  
pp. 1-11
Author(s):  
Velichka Traneva ◽  
Stoyan Tranev
Keyword(s):  
Comparative Analysis ◽  
Real Data ◽  
Intuitionistic Fuzzy Sets ◽  
Real Numbers ◽  
Data Set ◽  
Important Method ◽  
Ticket Sales ◽  
Intuitionistic Fuzzy ◽  
The One ◽  
First Time

Analysis of variance (ANOVA) is an important method in data analysis, which was developed by Fisher. There are situations when there is impreciseness in data In order to analyze such data, the aim of this paper is to introduce for the first time an intuitionistic fuzzy two-factor ANOVA (2-D IFANOVA) without replication as an extension of the classical ANOVA and the one-way IFANOVA for a case where the data are intuitionistic fuzzy rather than real numbers. The proposed approach employs the apparatus of intuitionistic fuzzy sets (IFSs) and index matrices (IMs). The paper also analyzes a unique set of data on daily ticket sales for a year in a multiplex of Cinema City Bulgaria, part of Cineworld PLC Group, applying the two-factor ANOVA and the proposed 2-D IFANOVA to study the influence of “ season ” and “ ticket price ” factors. A comparative analysis of the results, obtained after the application of ANOVA and 2-D IFANOVA over the real data set, is also presented.

scholarly journals Constructing Large-Scale Genetic Maps Using an Evolutionary Strategy Algorithm

Genetics ◽  
2003 ◽  
Vol 165 (4) ◽  
pp. 2269-2282
Author(s):  
D Mester ◽  
Y Ronin ◽  
D Minkov ◽  
E Nevo ◽  
A Korol
Keyword(s):  
Discrete Optimization ◽  
High Performance ◽  
Large Scale ◽  
Simulated Data ◽  
Real Data ◽  
Genetic Maps ◽  
Chromosome 1 ◽  
Evolutionary Strategy ◽  
Group A ◽  
The One

Abstract This article is devoted to the problem of ordering in linkage groups with many dozens or even hundreds of markers. The ordering problem belongs to the field of discrete optimization on a set of all possible orders, amounting to n!/2 for n loci; hence it is considered an NP-hard problem. Several authors attempted to employ the methods developed in the well-known traveling salesman problem (TSP) for multilocus ordering, using the assumption that for a set of linked loci the true order will be the one that minimizes the total length of the linkage group. A novel, fast, and reliable algorithm developed for the TSP and based on evolution-strategy discrete optimization was applied in this study for multilocus ordering on the basis of pairwise recombination frequencies. The quality of derived maps under various complications (dominant vs. codominant markers, marker misclassification, negative and positive interference, and missing data) was analyzed using simulated data with ∼50-400 markers. High performance of the employed algorithm allows systematic treatment of the problem of verification of the obtained multilocus orders on the basis of computing-intensive bootstrap and/or jackknife approaches for detecting and removing questionable marker scores, thereby stabilizing the resulting maps. Parallel calculation technology can easily be adopted for further acceleration of the proposed algorithm. Real data analysis (on maize chromosome 1 with 230 markers) is provided to illustrate the proposed methodology.

Predicting Ambulance Diverson

2010 ◽  
Vol 2 (1) ◽  
pp. 1-10 ◽  
Author(s):  
Abey Kuruvilla ◽  
Suraj M. Alexander
Keyword(s):  
Kansas City ◽  
Real Data ◽  
The United States ◽  
Time Of Day ◽  
Multinomial Regression ◽  
Predictive Tool ◽  
Persistent Problem ◽  
Cascading Effect ◽  
The One ◽  
Predictive Instrument

The high utilization level of emergency departments in hospitals across the United States has resulted in the serious and persistent problem of ambulance diversion. This problem is magnified by the cascading effect it has on neighboring hospitals, delays in emergency care, and the potential for patients’ clinical deterioration. We provide a predictive tool that would give advance warning to hospitals of the impending likelihood of diversion. We hope that with a predictive instrument, such as the one described in this article, hospitals can take preventive or mitigating actions. The proposed model, which uses logistic and multinomial regression, is evaluated using real data from the Emergency Management System (EM Systems) and 911 call data from Firstwatch® for the Metropolitan Ambulance Services Trust (MAST) of Kansas City, Missouri. The information in these systems that was significant in predicting diversion includes recent 911 calls, season, day of the week, and time of day. The model illustrates the feasibility of predicting the probability of impending diversion using available information. We strongly recommend that other locations, nationwide and abroad, develop and use similar models for predicting diversion.

A diffusion process to model generalized von Bertalanffy growth patterns: Fitting to real data

2010 ◽  
Vol 263 (1) ◽  
pp. 59-69 ◽  
Author(s):  
Patricia Román-Román ◽  
Desirée Romero ◽  
Francisco Torres-Ruiz
Keyword(s):  
Diffusion Process ◽  
Real Data ◽  
Growth Patterns ◽  
Von Bertalanffy
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