Modeling Crop Yield Distributions from Small Samples

Accurately modeling crop yield distributions is important for estimation of crop insurance premiums and farm risk-management decisions. A major challenge in the modeling has been due to small sample size. This study evaluated potentials of L-moments, a recent concept in mathematical statistics, in modeling crop yield distribution. Five candidate distributions were ranked for describing the wheat yields. The selected distribution was robust for small sample and was invariant to de-trending. The result was consistent with that from the maximum likelihood and goodness-of-fit method.Crop Production/Industries,

Operational Risk Management and Implications for Bank’s Economic Capital – a Case Study

In this paper we review the actual operational data of an anonymous Central European Bank, using two approaches described in the literature: the loss distribution approach and the extreme value theory (“EVT”). Within the EVT analysis, two estimation methods were applied; the standard maximum likelihood estimation method and the probability weighted method (“PWM”). Our results proved a heavy-tailed pattern of operational risk data consistent with the results documented by other researchers in this field. Additionally, our research demonstrates that the PWM is quite consistent even when the data is limited since our results provide reasonable and consistent capital estimates. From a policy perspective, it should be noted that banks from emerging markets such as Central Europe are exposed to these operational risk events and that successful estimates of the likely distribution of these risk events can be derived from more mature markets.operational risk, economic capital, Basel II, extreme value theory, probability weighted method

Nonparametric estimation when income is reported in bands and at points

We show how to estimate kernel density functions of distributions in which some of the responses are provided in brackets, by inverse probability weighting. We consider two cases, one where the data are CAR and where the data are not CAR. We show how the selection probabilities can be estimated by means of the EM algorithm without specifying a parametric distribution function for the variable. A Monte Carlo experiment shows that this procedure estimates the selection parameters fairly precisely. We apply these techniques to earnings data from South Africa’s first post-apartheid nationally representative survey, the 1994 October Household Survey.coarsening, bracket responses, EM algorithm, inverse probability weighting

Modeling electricity spot prices: Regime switching models with price-capped spike distributions

We calibrate Markov regime-switching (MRS) models to spot (log-)prices from two major power markets. We show that while the price-capped (or truncated) spike distributions do not give any advantage over the standard specification in case of moderately spiky markets (such as NEPOOL), they improve the fit and yield significantly different results in case of extremely spiky markets (such as the Australian NSW market).Electricity spot price; Markov regime-switching model; Price spike; Price cap; Truncated distribution

Novel Discrete Composite Distributions with Applications to Infectious Disease Data

It was observed that the number of cases and deaths for infectious diseases were associated with heavy-tailed power law distributions such as the Pareto distribution. While Pareto distribution was widely used to model the cases and deaths of infectious diseases, a major limitation of Pareto distribution is that it can only fit a given data set beyond a certain threshold. Thus, it can only model part of the data set. Thus, we proposed some novel discrete composite distributions with Pareto tails to fit the real infectious disease data. To provide necessary statistical inference for the tail behavior of the data, we developed a hypothesis testing procedure to test the tail index parameter. COVID-19 reported cases in Singapore and monkeypox reported cases in France were analyzed to evaluate the performance of the newly created distributions. The results from the analysis suggested that the discrete composite distributions could demonstrate competitive performance compared to the commonly used discrete distributions. Furthermore, the analysis of the tail index parameter can provide great insights into preventing and controlling infectious diseases

Implementing the multimodel generalized beta estimator in stata and its application

The multimodel generalized beta estimator (MGBE) described by von Hippel, Scarpino and Hola (2014) provides researchers with an improved way to estimate inequality from binned incomes. To extend the application of MGBE, the mgbe command is developed in Stata. In this report, the implementation and performance of mgbe are discussed.Statistic

Analytical and numerical approach to corporate operational risk modelling

Although The New Basel Accord gives the methodology for managing operational risk in financial institutions, corporate risk seems not to be recognized enough. In this Ph.D. thesis we make an attempt to put some insight into operational risk measurement in a non-financial corporation. The objective is to apply suitable results from insurance ruin theory to build a framework for measuring corporate operational risk and finding required capital charge.Corporate risk management; Operational risk; Actuarial risk theory; Ruin probability; Operational reserves;