scholarly journals On Modelling Extreme Damages from Natural Disasters in Kenya

2021 ◽  
Author(s):  
Carolyne Ogutu ◽  
Antony Rono
Keyword(s):  
Natural Disasters ◽  
Negative Binomial ◽  
Extreme Value Distribution ◽  
Likelihood Estimation ◽  
High Threshold ◽  
Frequency Of Occurrence ◽  
Probability Weighted Moments ◽  
Log Likelihood ◽  
Future Events ◽  
Generalised Pareto Distribution

We seek to develop a distribution to model the extreme damages resulting from Natural Disasters in Kenya.The distribution is based on the Compound Extreme Value Distribution, which takes into account both the distributions of the frequency of occurrence and magnitude of the events. Threshold modelling is employed, where the extreme damages are identified as the points that lie above a sufficiently high threshold. The distribution of the number of the exceedance is found to be Negative Binomial, while that of the severity is approximated by a Generalised Pareto Distribution. Maximum likelihood estimation is used to estimate the parameters, and the log-likelihood is maximised using numerical methods. Probability weighted moments estimation is used to determine the starting values for the iterations. Prediction study is then carried out to investigate the performance of the proposed distribution in predicting future events.

scholarly journals On Compound Distributions for Natural Disaster Modelling in Kenya

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Antony Rono ◽  
Carolyne Ogutu ◽  
Patrick Weke
Keyword(s):  
Natural Disasters ◽  
Pareto Distribution ◽  
Negative Binomial ◽  
Threshold Model ◽  
Generalized Pareto Distribution ◽  
Extreme Value Distribution ◽  
Extreme Value ◽  
Generalized Pareto ◽  
Compound Distribution ◽  
Poor Infrastructure

Kenyan communities are exposed to natural disasters by an amalgamation of factors such as poverty, aridity, and settlements in areas susceptible to natural disasters or in areas with poor infrastructure. This is expected to increase due to the effects of climate change. In an attempt to explain some of these variabilities, we model the extreme damages from natural disasters in Kenya by developing a compound distribution that takes into account both the frequency and the severity of the extreme events. The resulting distribution is based on a threshold model and compound extreme value distribution. For frequency of events exceeding a threshold of 150,000, we found that it follows a negative binomial distribution, while severity of exceedance follows a generalized Pareto distribution. This distribution fits the data well and is found to be a better model for natural disasters in Kenya than the traditional extreme value threshold model.

scholarly journals Assessing the Performance of the Discrete Generalised Pareto Distribution in Modelling Non-Life Insurance Claims

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
S. K.-B. Dzidzornu ◽  
R. Minkah
Keyword(s):  
Life Insurance ◽  
Pareto Distribution ◽  
Negative Binomial ◽  
Likelihood Estimation ◽  
Claim Data ◽  
Information Criteria ◽  
Distribution Data ◽  
Insurance Claims ◽  
Frequency Method ◽  
Generalised Pareto Distribution

The generalised Pareto distribution (GPD) offers a family of probability spaces which support threshold exceedances and is thus suitable for modelling high-end actuarial risks. Nonetheless, its distributional continuity presents a critical limitation in characterising data of discrete forms. Discretising the GPD, therefore, yields a derived distribution which accommodates the count data while maintaining the essential tail modelling properties of the GPD. In this paper, we model non-life insurance claims under the three-parameter discrete generalised Pareto (DGP) distribution. Data for the study on reported and settled claims, spanning the period 2012–2016, were obtained from the National Insurance Commission, Ghana. The maximum likelihood estimation (MLE) principle was adopted in fitting the DGP to yearly and aggregated data. The estimation involved two steps. First, we propose a modification to the μ and μ + 1 frequency method in the literature. The proposal provides an alternative routine for generating initial estimators for MLE, in cases of varied count intervals, as is a characteristic of the claim data under study. Second, a bootstrap algorithm is implemented to obtain standard errors of estimators of the DGP parameters. The performance of the DGP is compared to the negative binomial distribution in modelling the claim data using the Akaike and Bayesian information criteria. The results show that the DGP is appropriate for modelling the count of non-life insurance claims and provides a better fit to the regulatory claim data considered.

scholarly journals Identifying Stabilising Effects on Survey Based Life Satisfaction Using Quasi-maximum Likelihood Estimation

2021 ◽  
Author(s):  
Johannes Klement
Keyword(s):  
Life Satisfaction ◽  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Negative Binomial ◽  
Measurement Instrument ◽  
Likelihood Estimation ◽  
Satisfaction Scale ◽  
Quasi Maximum Likelihood ◽  
The Stability

AbstractTo which extent do happiness correlates contribute to the stability of life satisfaction? Which method is appropriate to provide a conclusive answer to this question? Based on life satisfaction data of the German SOEP, we show that by Negative Binomial quasi-maximum likelihood estimation statements can be made as to how far correlates of happiness contribute to the stabilisation of life satisfaction. The results show that happiness correlates which are generally associated with a positive change in life satisfaction, also stabilise life satisfaction and destabilise dissatisfaction with life. In such as they lower the probability of leaving positive states of life satisfaction and increase the probability of leaving dissatisfied states. This in particular applies to regular exercise, volunteering and living in a marriage. We further conclude that both patterns in response behaviour and the quality of the measurement instrument, the life satisfaction scale, have a significant effect on the variation and stability of reported life satisfaction.

scholarly journals Evaluating the Observed Log-Likelihood Function in Two-Level Structural Equation Modeling with Missing Data: From Formulas to R Code

Psych ◽  
2021 ◽  
Vol 3 (2) ◽  
pp. 197-232
Author(s):  
Yves Rosseel
Keyword(s):  
Structural Equation ◽  
Structural Equation Models ◽  
Likelihood Function ◽  
Likelihood Estimation ◽  
Missing At Random ◽  
Equation Modeling ◽  
Computationally Efficient ◽  
Log Likelihood ◽  
Efficient Expression ◽  
Special Case

This paper discusses maximum likelihood estimation for two-level structural equation models when data are missing at random at both levels. Building on existing literature, a computationally efficient expression is derived to evaluate the observed log-likelihood. Unlike previous work, the expression is valid for the special case where the model implied variance–covariance matrix at the between level is singular. Next, the log-likelihood function is translated to R code. A sequence of R scripts is presented, starting from a naive implementation and ending at the final implementation as found in the lavaan package. Along the way, various computational tips and tricks are given.

scholarly journals Maximum Product of Spacing Parameter Estimation of Gompertz Rayleigh Distribution and Application to Rainfall Datasets

2021 ◽  
pp. 41-59
Author(s):  
Hussein Ahmad Abdulsalam ◽  
Sule Omeiza Bashiru ◽  
Alhaji Modu Isa ◽  
Yunusa Adavi Ojirobe
Keyword(s):  
Goodness Of Fit ◽  
Negative Binomial ◽  
Likelihood Estimation ◽  
Statistical Properties ◽  
Rainfall Data ◽  
Parameter Estimates ◽  
Data Sets ◽  
Unknown Parameters ◽  
Exponentiated Weibull ◽  
Integrated Hazard

Gompertz Rayleigh (GomR) distribution was introduced in an earlier study with few statistical properties derived and parameters estimated using only the most common traditional method, Maximum Likelihood Estimation (MLE). This paper aimed at deriving more statistical properties of the GomR distribution, estimating the three unknown parameters via a competitive method, Maximum Product of Spacing (MPS) and evaluating goodness of fit using rainfall data sets from Nigeria, Malaysia and Argentina. Properties of statistical distributions including distribution of smallest and largest order statistics, cumulative or integrated hazard function, odds function, rth non-central moments, moment generating function, mean, variance and entropy measures for GomR distribution were explicitly derived. The fitted data sets reveal the flexibility of GomR distribution over other distributions been compared with. Simulation study was used to evaluate the consistency, accuracy and unbiasedness of the GomR distribution parameter estimates obtained from the method of MPS. The study found that GomR distribution could not provide a better fit for Argentine rainfall data but it was the best distribution for the rainfall data sets from Nigeria and Malaysia in comparison with the distributions; Generalized Weibull Rayleigh (GWR), Exponentiated Weibull Rayleigh (EWR), Type (II) Topp Leone Generalized Inverse Rayleigh (TIITLGIR), Kumarawamy Exponential Inverse Raylrigh (KEIR), Negative Binomial Marshall-Olkin Rayleigh (NBMOR) and Exponentiated Weibull (EW). Furthermore, the estimates from MPSE were consistent as the sample size increases but not as efficient as those from MLE.

scholarly journals Modelling asthma cases by count analysis approach: Poisson INGARCH and Negative Binomial INGARCH

MATEMATIKA ◽  
2020 ◽  
Vol 36 (1) ◽  
pp. 15-30
Author(s):  
'Aaishah Radziah Jamaludin ◽  
Fadhilah Yusof ◽  
Suhartono Suhartono
Keyword(s):  
Negative Binomial ◽  
Integral Transform ◽  
Rapid Development ◽  
Information Criterion ◽  
Analysis Approach ◽  
Model Assessment ◽  
Link Function ◽  
Estimation Model ◽  
Pearson Residuals ◽  
Log Likelihood

Johor Bahru with its rapid development where pollution is an issue that needs to be considered because it has contributed to the number of asthma cases in this area. Therefore, the goal of this study is to investigate the behaviour of asthma disease in Johor Bahru by count analysis approach namely; Poisson Integer Generalized Autoregressive Conditional Heteroscedasticity (Poisson-INGARCH) and Negative Binomial INGARCH (NB-INGARCH) with identity and log link function. Intervention analysis was conducted since the outbreak in the asthma data for the period of July 2012 to July 2013. This occurs perhaps due to the extremely bad haze in Johor Bahru from Indonesian fires. The estimation of the parameter will be done by quasi-maximum likelihood estimation. Model assessment was evaluated from the Pearson residuals, cumulative periodogram, the probability integral transform (PIT) histogram, log-likelihood value, Akaike’s Information Criterion (AIC) and Bayesian information criterion (BIC). Our result shows that NB-INGARCH with identity and log link function is adequate in representing the asthma data with uncorrelated Pearson residuals, higher in log likelihood, the PIT exhibits normality yet the lowest AIC and BIC. However, in terms of forecasting accuracy, NB-INGARCH with identity link function performed better with the smaller RMSE (8.54) for the sample data. Therefore, NB-INGARCH with identity link function can be applied as the prediction model for asthma disease in Johor Bahru. Ideally, this outcome can assist the Department of Health in executing counteractive action and early planning to curb asthma diseases in Johor Bahru.

scholarly journals Comparing of Car-Bym, Generalized Poisson dan Negative Binomial on Tuberculosis Data in Banyumas Districs

2021 ◽  
Vol 5 (1) ◽  
pp. 130-140
Author(s):  
Jajang Jajang ◽  
Budi Pratikno ◽  
Mashuri Mashuri
Keyword(s):  
Parameter Estimation ◽  
Maximum Likelihood ◽  
Count Data ◽  
Degrees Of Freedom ◽  
Negative Binomial ◽  
Likelihood Estimation ◽  
Poisson Model ◽  
Generalized Poisson ◽  
Central Java ◽  
Area Data

In 2019 the number of people with TB (Tuberculosis) in Banyumas, Central Java, is high (1,910 people have been detected with TB). The number of people infected Tuberculosis (TB) in Banyumas is the count data and it is also the area data. In modeling, the parameter estimation and characteristic of the data need to be considered. Here, we studied comparing Generalized Poisson (GP), negative binomial (NB), and Poisson and CAR.BYM model for TB cases in Banyumas. Here, we use two methods for parameter estimation, maximum likelihood estimation (MLE) and Bayes. The MLE is used for GP and NB models, whereas Bayes is used for Poisson and CAR-BYM. The results showed that Poisson model detected overdispersion where deviance value is 67.38 for 22 degrees of freedom. Therefore, ratio of deviance to degrees of freedom is 3.06 (>1). This indicates that there was overdispersion. The folowing GP, NB, Poisson-Bayes and CAR-BYM are used to modeling TB data in Banyumas and we compare their RMSE. With refer to RMES criteria, we found that CAR-BYM is the best model for modeling TB in Banyumas because its RMSE is smallest.

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