scholarly journals Modeling and Risk Analysis Using Parametric Distributions with an Application in Equity-Linked Securities

2020 ◽  
Vol 2020 ◽  
pp. 1-20 ◽  
Author(s):  
Sun-Yong Choi ◽  
Ji-Hun Yoon
Keyword(s):  
Risk Analysis ◽  
Goodness Of Fit ◽  
Risk Measures ◽  
Information Criteria ◽  
Stock Index ◽  
Distribution Model ◽  
Goodness Of Fit Test ◽  
Stock Indices ◽  
Management Concepts ◽  
Best Fit

In this study, we model the returns of a stock index using various parametric distribution models. There are four indices used in this study: HSCEI, KOSPI 200, S&P 500, and EURO STOXX 50. We applied 12 distributions to the data of these stock indices—Cauchy, Laplace, normal, Student’s t, skew normal, skew Cauchy, skew Laplace, skew Student’s t, hyperbolic, normal inverse Gaussian, variance gamma, and general hyperbolic—for the parametric distribution model. In order to choose the best-fit distribution for describing the stock index, we used the information criteria, goodness-of-fit test, and graphical tail test for each stock index. We estimated the value-at-risk (VaR), one of the most popular management concepts in the area of risk management, for the return of stock indices. Furthermore, we applied the parametric distributions to the risk analysis of equity-linked securities (ELS) as they are a very popular financial product on the Korean financial market. Relevant risk measures, such as VaR and conditional tail expectation, are calculated using various distributions. For calculating the risk measures, we used Monte Carlo simulations under the best-fit distribution. According to the empirical results, investing in ELS is more risky than investing in securities, and the risk measure of the ELS heavily depends on the type of security.

Empirical comparison of skewed t-copula models for insurance and financial data

2020 ◽  
Vol 15 (4) ◽  
pp. 351-361
Author(s):  
Liwei Huang ◽  
Arkady Shemyakin
Keyword(s):  
Bayesian Estimation ◽  
Goodness Of Fit ◽  
Model Performance ◽  
Information Criteria ◽  
Stock Index ◽  
Likelihood Method ◽  
Special Importance ◽  
Copula Model ◽  
Technical Problems ◽  
T Copula

Skewed t-copulas recently became popular as a modeling tool of non-linear dependence in statistics. In this paper we consider three different versions of skewed t-copulas introduced by Demarta and McNeill; Smith, Gan and Kohn; and Azzalini and Capitanio. Each of these versions represents a generalization of the symmetric t-copula model, allowing for a different treatment of lower and upper tails. Each of them has certain advantages in mathematical construction, inferential tools and interpretability. Our objective is to apply models based on different types of skewed t-copulas to the same financial and insurance applications. We consider comovements of stock index returns and times-to-failure of related vehicle parts under the warranty period. In both cases the treatment of both lower and upper tails of the joint distributions is of a special importance. Skewed t-copula model performance is compared to the benchmark cases of Gaussian and symmetric Student t-copulas. Instruments of comparison include information criteria, goodness-of-fit and tail dependence. A special attention is paid to methods of estimation of copula parameters. Some technical problems with the implementation of maximum likelihood method and the method of moments suggest the use of Bayesian estimation. We discuss the accuracy and computational efficiency of Bayesian estimation versus MLE. Metropolis-Hastings algorithm with block updates was suggested to deal with the problem of intractability of conditionals.

scholarly journals Results of the Verification of the Statistical Distribution Model of Microseismicity Emission Characteristics

2016 ◽  
Vol 61 (3) ◽  
pp. 489-496
Author(s):  
Aleksander Cianciara
Keyword(s):  
Distribution Function ◽  
Weibull Distribution ◽  
Goodness Of Fit ◽  
Cumulative Distribution Function ◽  
Statistical Distribution ◽  
Cumulative Distribution ◽  
Distribution Model ◽  
Emission Characteristics ◽  
Goodness Of Fit Test ◽  
Empirical Cumulative Distribution Function

Abstract The paper presents the results of research aimed at verifying the hypothesis that the Weibull distribution is an appropriate statistical distribution model of microseismicity emission characteristics, namely: energy of phenomena and inter-event time. It is understood that the emission under consideration is induced by the natural rock mass fracturing. Because the recorded emission contain noise, therefore, it is subjected to an appropriate filtering. The study has been conducted using the method of statistical verification of null hypothesis that the Weibull distribution fits the empirical cumulative distribution function. As the model describing the cumulative distribution function is given in an analytical form, its verification may be performed using the Kolmogorov-Smirnov goodness-of-fit test. Interpretations by means of probabilistic methods require specifying the correct model describing the statistical distribution of data. Because in these methods measurement data are not used directly, but their statistical distributions, e.g., in the method based on the hazard analysis, or in that that uses maximum value statistics.

scholarly journals MODELING APPLIED TO SOWING DATE OF IRRIGATED MAIZE

2018 ◽  
Vol 17 (2) ◽  
pp. 201
Author(s):  
IVALDO MARTINS BOGGIONE ◽  
CAMILO DE LELIS TEIXEIRA DE ANDRADE ◽  
JOÃO CARLOS FERREIRA BORGES JÚNIOR ◽  
JOÃO HERBERT MOREIRA VIANA
Keyword(s):  
Zea Mays ◽  
Risk Analysis ◽  
Goodness Of Fit ◽  
Zea Mays L ◽  
Sprinkler Irrigation ◽  
Sowing Date ◽  
Minas Gerais ◽  
Goodness Of Fit Test ◽  
Yield Data ◽  
Maize Crop

 ABSTRACT – In Brazil, the rainfed maize crop may undergo yield breaks due to uncertainties in the rainfall distribution. Irrigation can be a management alternative that, however, requires evaluation and planning to be helpful. The objective of this work was to analyze the simulated yield data of irrigated maize in counties of Minas Gerais state, Brazil. The CSM-CERES-Maize model was used to simulated weekly sowings of maize considering optimum agronomic conditions. A sprinkler irrigation scheme with 80% efficiency was used with automatic applications when the crop withdrew 50% of the soil available water. The harvest was scheduled to happen automatically when the crop had reached physiological maturity. The results were statistically analyzed for each county, based on goodness of fit test, ANOVA, Tukey’s test and risk analysis (stochastic dominance). The most promising sowing period was from January 16 to March 27 for all locations, except for Janaúba, for which the best sowing window was from November 14 to January 2. The treatments of highest average simulated maize yield stochastically dominated the other treatments evaluated. The CSM-CERES-Maize model proved to be a useful tool to help making decision in irrigated maize crop systems.Keywords: Zea mays L., CSM-CERES-Maize, DSSAT, risk analysis. MODELAGEM APLICADA A DATAS DE SEMEADURA DE MILHO IRRIGADO  RESUMO – No Brasil, a produção de milho de sequeiro pode sofrer quebras de rendimento devido a irregularidades na distribuição de chuvas. A irrigação pode ser uma alternativa de manejo que, todavia, requer avaliação e planejamento para ser benéfica. O objetivo deste trabalho foi analisar a produtividade simulada de milho irrigado em municípios do estado de Minas Gerais, Brasil. O modelo CSM-CERES-Maize foi utilizado para simular semeaduras semanais de milho, assumindo condições agronômicas ótimas. Considerou-se um esquema de irrigação por aspersão com 80% de eficiência, com aplicações automáticas quando a planta extraísse 50% da água disponível do solo. A colheita foi programada para acontecer automaticamente quando a cultura atingisse a maturidade fisiológica. Os resultados foram estatisticamente analisados para cada município, com base em teste de aderência, ANOVA, teste de Tukey e análise de risco (dominância estocástica). O período de semeadura mais promissor foi de 16 de janeiro a 27 de março, para todos os locais, exceto Janaúba, em que a melhor janela de semeadura foi de 14 de novembro a 2 de janeiro. Os tratamentos de maior rendimento médio simulado de milho dominaram estocasticamente os demais tratamentos avaliados. O modelo CSM-CERES-Maize demonstrou ser uma ferramenta útil para auxiliar na tomada de decisão em sistemas de produção de milho irrigado.Palavras-chave: Zea mays L., CSM-CERES-Maize, DSSAT, análise de risco.

scholarly journals Age Distribution Model For GCC Countries

2011 ◽  
Vol 8 (11) ◽  
Author(s):  
Shafiqur Rahman
Keyword(s):  
Goodness Of Fit ◽  
Census Data ◽  
Age Distribution ◽  
Developed Countries ◽  
Distribution Model ◽  
School Age Children ◽  
Population Census ◽  
Goodness Of Fit Test ◽  
Chi Square ◽  
Gcc Countries

Efficient and reliable estimates of the proportions of population at different age levels are essential for making quality budget of any developing or developed nation. These estimates are obtained from the best-fitted age distribution model and can be used to find the number of school age children, number of pensioners etc. Past population census data of GCC countries are analyzed to find the best-fitted age distribution model applying chi-square goodness of fit test and model selection criteria and observed that the age distribution of most of the GCC countries is exponential. A comparative study of the age distributions of six GCC countries with some developed countries is also provided.

scholarly journals Flood Flow Probability Distribution Model Selection on Niger/Benue River Basins in Nigeria

2021 ◽  
pp. 76-94
Author(s):  
Itolima Ologhadien
Keyword(s):  
Probability Distribution ◽  
Goodness Of Fit ◽  
River Basins ◽  
Flood Frequency ◽  
Flood Frequency Analysis ◽  
Distribution Model ◽  
Distribution Models ◽  
Type Iii ◽  
Pearson Type ◽  
Best Fit

Flood frequency analysis is a crucial component of flood risk management which seeks to establish a quantile relationship between peak discharges and their exceedance (or non-exceedance) probabilities, for planning, design and management of infrastructure in river basins. This paper evaluates the performance of five probability distribution models using the method of moments for parameter estimation, with five GoF-tests and Q-Q plots for selection of best –fit- distribution. The probability distributions models employed are; Gumbel (EV1), 2-parameter lognormal (LN2), log Pearson type III (LP3), Pearson type III(PR3), and Generalised Extreme Value( GEV). The five statistical goodness – of – fit tests, namely; modified index of agreement (Dmod), relative root mean square error (RRMSE), Nash – Sutcliffe efficiency (NSE), Percent bias (PBIAS), ratio of RMSE and standard deviation of the measurement (RSR) were used to identify the most suitable distribution models. The study was conducted using annual maximum series of nine gauge stations in both Benue and Niger River Basins in Nigeria. The study reveals that GEV was the best – fit distribution in six gauging stations, LP3 was best – fit distribution in two gauging stations, and PR3 is best- fit distribution in one gauging station. This study has provided a significant contribution to knowledge in the choice of distribution models for predicting extreme hydrological events for design of water infrastructure in Nigeria. It is recommended that GEV, PR3 and LP3 should be considered in the development of regional flood frequency using the existing hydrological map of Nigeria.

Fitting The Best–Fit Distribution For The Hourly Rainfall Amount In The Wilayah Persekutuan

2012 ◽  
Author(s):  
Fadhilah Y. ◽  
Zalina Md. ◽  
Nguyen V–T–V. ◽  
Suhaila S. ◽  
Zulkifli Y.
Keyword(s):  
Maximum Likelihood ◽  
Goodness Of Fit ◽  
Rainfall Amount ◽  
Likelihood Method ◽  
Exceedance Probability ◽  
Parameter Estimates ◽  
Goodness Of Fit Test ◽  
Hourly Rainfall ◽  
Best Fit ◽  
Mixed Exponential Distribution

Dalam mengenal pasti model yang terbaik untuk mewakili taburan jumlah hujan bagi data selang masa satu jam di 12 stesen di Wilayah Persekutuan empat taburan digunakan iaitu Taburan Eksponen, Gamma, Weibull dan Gabungan Eksponen. Parameter–parameter dianggar menggunakan kaedah kebolehjadian maksimum. Model yang terbaik dipilih berdasarkan nilai minimum yang diperolehi daripada ujian–ujian kebagusan penyuaian yang digunakan dalam kajian ini. Ujian ini dipertahankan lagi dengan plot kebarangkalian dilampaui. Taburan Gabungan Eksponen di dapati paling baik untuk mewakili taburan jumlah hujan dalam selang masa satu jam. Daripada anggaran parameter bagi taburan Gabungan Eksponen ini, boleh diterjemah bahawa jumlah hujan tertinggi yang direkodkan diperolehi daripada hujan yang dikategorikan sebagai hujan lebat, walaupun hujan renyai–renyai berlaku lebih kerap. Kata kunci: Jumlah hujan dalam selang masa sejam, ujian kebagusan penyuaian, kebolehjadian maksimum In determining the best–fit model for the hourly rainfall amounts for the twelve stations in the Wilayah Persekutuan, four distributions namely, the Exponential, Gamma, Weibull and Mixed–Exponential were used. Parameters for each distribution were estimated using the maximum likelihood method. The best–fit model was chosen based upon the minimum error produced by the goodness–offit tests used in this study. The tests were justified further by the exceedance probability plot. The Mixed–Exponential was found to be the most appropriate distribution in describing the hourly rainfall amounts. From the parameter estimates for the Mixed–Exponential distribution, it could be implied that most of the hourly rainfall amount recorded were received from the heavy rainfall even though there was a high occurrences of light rainfall. Key words: Hourly rainfall amount, goodness-of-fit test, exceedance probability, maximum likelihood

scholarly journals Model Efficiency and Uncertainty in Quantile Estimation of Loss Severity Distributions

Risks ◽  
2019 ◽  
Vol 7 (2) ◽  
pp. 55
Author(s):  
Vytaras Brazauskas ◽  
Sahadeb Upretee
Keyword(s):  
Value At Risk ◽  
Goodness Of Fit ◽  
Risk Measures ◽  
Probability Distributions ◽  
Simulated Data ◽  
Information Criteria ◽  
Asymptotic Distributions ◽  
Parametric Estimation ◽  
Goodness Of Fit Tests ◽  
Transfer Strategies

Quantiles of probability distributions play a central role in the definition of risk measures (e.g., value-at-risk, conditional tail expectation) which in turn are used to capture the riskiness of the distribution tail. Estimates of risk measures are needed in many practical situations such as in pricing of extreme events, developing reserve estimates, designing risk transfer strategies, and allocating capital. In this paper, we present the empirical nonparametric and two types of parametric estimators of quantiles at various levels. For parametric estimation, we employ the maximum likelihood and percentile-matching approaches. Asymptotic distributions of all the estimators under consideration are derived when data are left-truncated and right-censored, which is a typical loss variable modification in insurance. Then, we construct relative efficiency curves (REC) for all the parametric estimators. Specific examples of such curves are provided for exponential and single-parameter Pareto distributions for a few data truncation and censoring cases. Additionally, using simulated data we examine how wrong quantile estimates can be when one makes incorrect modeling assumptions. The numerical analysis is also supplemented with standard model diagnostics and validation (e.g., quantile-quantile plots, goodness-of-fit tests, information criteria) and presents an example of when those methods can mislead the decision maker. These findings pave the way for further work on RECs with potential for them being developed into an effective diagnostic tool in this context.

scholarly journals Statistical Distribution of Rainfall in Kurdistan-Iraq Region

2020 ◽  
Vol 30 (4) ◽  
pp. 18
Author(s):  
Meeran Akram Fawzee ◽  
Samira M. Salh ◽  
Slahaddin A. Ahmed
Keyword(s):  
Goodness Of Fit ◽  
Extreme Value ◽  
Rainfall Amount ◽  
Statistical Distribution ◽  
Rainfall Series ◽  
Goodness Of Fit Test ◽  
Chi Square ◽  
Anderson Darling ◽  
Best Fit ◽  
General Extreme Value

Study the statistical distribution for rainfall is important to know the behaviour of the rainfall series and to know the most frequently rainfall amount in each month. Five statistical distribution were applied on Sulaimani, Erbil and Duhok rainfall series for the period (1941-2017) except Duhok (1944-2017). These distributions were Gamma(3P), Weibul(3P), Earlang (3P), Normal and General extreme value. Kolmogrove-Semirnov, Anderson-Darling and Chi-Square goodness of fit test were used to know the best fit distribution from these five distributions.

scholarly journals Modeling of Nigeria’s Economic Growth Rate: A Probability Distribution Fitting Approach

2018 ◽  
pp. 1-17
Author(s):  
Eke, Charles N ◽  
Osuji, George Amaeze ◽  
Nwosu, Dozie Felix
Keyword(s):  
Economic Growth ◽  
Growth Rate ◽  
Probability Distribution ◽  
Goodness Of Fit ◽  
Laplace Distribution ◽  
Information Criteria ◽  
Logistic Distribution ◽  
Goodness Of Fit Test ◽  
Economic Growth Rate ◽  
Generalized Logistic Distribution

This study examined the probability distribution that best described the quarterly economic growth rate of Nigeria between 1960- 2015. The study collected secondary data from Central Bank of Nigeria (CBN) Statistical Bulletin 2015 on Gross Domestic Product to compute the economic growth rate of Nigeria. Six theoretical statistical distributions were fitted via Normal Distribution, Logistic Distribution, Laplace Distribution, Cauchy Distribution, Gumbel (Largest Extreme Value) Distribution and Generalized Logistic Distribution. The Laplace Distribution fitted the data as confirmed by Kolmogorov Simonov goodness of fit test, Akaike Information Criteria and Bayes Information Criteria. The probabilities of economic growth rate behaviours were obtained from the best fit distribution. The analysis showed that the chance of obtaining a negative quarterly economic growth rate is 28%. The chance of an economic recession is 8%. Also, the probability of having a positive single digit quarterly economic growth rate is 46%. In addition, having a double digit positive quarterly economic growth rate is 26%.  

scholarly journals Statistical Examination of Uncaria gambir Roxb Drying Modeling

2020 ◽  
Vol 9 (2) ◽  
pp. 379-382
Keyword(s):  
Root Mean Square Error ◽  
Design Process ◽  
Goodness Of Fit ◽  
Mean Square ◽  
Air Velocity ◽  
Statistical Parameters ◽  
Goodness Of Fit Test ◽  
Chi Square ◽  
Drying Conditions ◽  
Best Fit

This study investigates the drying modeling of Uncaria gambir Roxb using convective desiccant examined by statistical parameters. Three types of drying modeling are investigated, i.e. the Newton, Page and Henderson-Pabis models. The drying conditions of Uncaria gambir Roxb were set at 35oC, 45oC and 55oC and air velocity of 1.2 m/s. The results show that the Page modeling is the best fit model for this investigation based on values of R2 (coefficient of determinant), RMSE (root mean square error) and χ2 (chi-square) goodness of fit test derived from (MR) moisture ratio equation. The Page modeling shows R2 value nearest to unity and lowest values of RMSE and χ2 are obtained for all given temperatures (35oC, 45oC and 55oC) at air velocity of 1.2 m/s. The drying modeling is useful for optimization in design process encountered with product quality and cost of production.

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