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In this work, we discuss constricting a mathematical formula based on a survival function. This formula has a basic parameter called a transmuted parameter. In addition, experimenting with this formula within Pareto distribution. The process of this production includes applying this formula to lifetime distributions. So the objective of this research is to formulate a distribution that is more flexible and accurate. A new model gives more accurate results on the application of data. The aim of the research study is to bring the transmuted survival Pareto distribution to closer to the Normal distribution. The probability density function, the probability cumulative function, and hazard function were extracted also, explaining the shapes of these functions for the model. Furthermore, derived the mathematical and statistical characteristics of the model. This model's parameters are also estimated using a classical method (Maximum Likelihood estimation method). [ABSTRACT FROM AUTHOR]

Having insurance could be minimized financial losses. Insurance companies must carry out proper risk management as insurance product providers. The amount of risk or loss experienced by policyholders is the size of the claim. In measuring risk, for the assumption of regular events, a measurement using the Value at Risk (VaR) is generally used. However, the size of claims is sometimes in different conditions or circumstances. There are times when extensive claims with a minor frequency significantly impact the insurance company. Therefore, in this paper, a significant claims analysis will be carried out using extreme value theory. The peaks over threshold (POT) approach is applied to specialize it, and The Generalized Pareto Distribution will be used to model it. The automated Threshold Selection Method will be used to select the threshold based on the distribution of the difference of parameter estimates when the threshold is changed and apply it to published claim severity. The Kolmogorov-Smirnov test will be used to test the threshold. The threshold value obtained is used to measure the risk with the value at risk, which will be used in calculating the reserve for claims. In applying the method, the claim size data is used for asset insurance with occupation code 293 (trading and storage) and occupation 297 (private buildings), which occurred from 20l0-20l6. With a significance level of 0.05, 293 occupation data it is modeled following the GP distribution with the parameters ξ ^ = 1230 , σ ^ = 2811 × 10 7 and threshold u = 3,745 billion, for 297 occupation data modeled following the GP distribution with the parameter ξ ^ = 0.935 , σ ^ = 1,733 × 10 7 and threshold u = 913 million. The VaR risk is used to determine the risk value of the claim distribution. As an illustration, the claim reserve scheme is based on the VaR value. [ABSTRACT FROM AUTHOR]

Extreme Value Theory (EVT) is one of the methods in statistical modelling to obtain the probabilities and frequencies associated with extreme situations in finance. This approach focuses on extreme values and can provide a good estimate for the risk model. In this study, Generalized Pareto Distribution (GPD) is employed to model extreme returns in the cryptocurrency market from Jan, 2019 to Dec, 2021. The results found that Bitcoin is less volatile compared to other cryptocurrencies. Ethereum can be viewed as a risky cryptocurrency in this research. [ABSTRACT FROM AUTHOR]

In this research, the method of synthesis of Pareto distributions of the first type and amputated ace was used to obtain amore flexible distribution of single distributions in the representation of data of complex phenomena and then derived its characteristics (decentralized moments, central moments, variance, torsion coefficient, flattening coefficient, median and mode), and its parameters were estimated in four ways, namely (Maximum Likelihood, moments, fragmentary capabilities and Bayes estimator (Jeffrey method)), and the conclusion was made By using different hypothetical values for the parameters and four different sizes for the samples, namely (100,50,25), the experiment was repeated (1000) times, and using the MSE) criterion to compare the results of the estimate that the torque and bayes methods compete for preference. [ABSTRACT FROM AUTHOR]

An earthquake is a big disaster that might cause a large amount of loss. Various ways had been proposed to overcome this situation, including the usage of catastrophe bonds. In this study, we propose an earthquake catastrophe bond in which both the coupon payment and principal payment are affected by the occurrence of earthquakes during the period. The pricing of this bond consists of several steps as follows: (1) obtain the earthquake data, (2) model the probability distribution of earthquake magnitude and depth, (3) propose the catastrophe bond's payment structure, and (4) derive the price formula. A numerical study using the data of earthquakes around Java and Sulawesi, Indonesia, is provided. We find that these data can be modeled well using Generalized Extreme Value (GEV) distribution, Rayleigh distribution, and Generalized Pareto distribution. Consequently, the price of catastrophe bonds can be determined using these distribution. [ABSTRACT FROM AUTHOR]

In this research, some of Pareto properties from the first class are studied beside some of its theories and Pareto distribution parameters were obtained using a median amount. The amount of shape parameter contains a very complex model and its properties are difficult to know. In this paper, we approximated the mean and the variance using Tyler series of second degree derivation to obtain a mathematical model. [ABSTRACT FROM AUTHOR]

In this paper, the reliability system R = P(X1 < Y < X2), of the stress-strength model was derived having strength (Y) subject to two stresses X1 and X2 follows the two parameters Rayleigh - Pareto distribution such as δ (scale) known and λ (shape) unknown parameters. We estimate the reliability function by using three estimation methods as maximum likelihood (ML), Percentile estimation (PE), and two shrinkage methods such that Shrinkage weight Estimator (SMW), and Shrinkage Function Estimator (SMF). To obtain the best estimate of the reliability function by using the Monte Carlo method depend on mean square error (MSE) criteria. The comparison showed that the (SMW) method is the best among the other methods. [ABSTRACT FROM AUTHOR]

This study is aimed to extract extreme rainfall data using Peak over Threshold (POT) method. The method would be used in conjunction with the generalized Pareto distribution (GPD) model. Daily rainfall data in the northern region of Peninsular Malaysia obtained from the Department of Irrigation and Drainage Malaysia (DID) for the period 1999 to 2019 is used. The mean residual life plot and parameter stability plot are used to choose a suitable threshold. The problem of choosing a suitable threshold for the extraction of extreme rainfall data is addressed by comparing the threshold to the constant threshold and the marginal threshold. The Maximum Likelihood Estimator (MLE) is used to estimate the parameters. Diagnostic plots and the return level are determined to confirm the suitability of the adapted model. According to the analysis, the selected constant threshold is 42 mm and the selected marginal threshold for all stations are varies from 38 mm to 48 mm. Generally, the maximum daily rainfall at all stations increases steadily during a higher return period. Over the next 25 years, the maximum daily rainfall amount is expected to return to all stations. [ABSTRACT FROM AUTHOR]

In many real-world problems, the phenomena of interest are continuous in nature and modeled through well-established continuous probability distributions, but it often occurs that observed values are actually discrete and then it would be more appropriate to use a (multivariate) discrete distribution generated from the underlying continuous model, which preserves one or more of its important features. In this work, we illustrate the genesis and properties of two bivariate discrete distributions that can be derived as discrete counterparts to a bivariate continuous Pareto distribution. The two discrete probability distributions preserve the expression of either 1) the joint density function or 2) the joint survival function of the parent distribution at each pair of non-negative integers. Their joint and marginal probability mass functions are derived and compared; the expressions for their bivariate failure rate vectors are also obtained. This study reveals how the second discrete analog is easier to handle with respect to the first one, whose expression of the probability mass function involves the Riemann zeta function. [ABSTRACT FROM AUTHOR]

The Pareto distributions are applied in many areas of research, such as astronomy, bibliometrics, biology, demography, insurance and risk management. In this paper, we compare the performance of the asymptotic confidence intervals for the Pareto shape parameter based on asymptotic distributions of the maximum likelihood and moment estimators. A simulation study is used to compare these confidence intervals via their coverage probabilities. [ABSTRACT FROM AUTHOR]

In this paper, a new family of distributions are introduced biased on Weibull Lindley (WL) distribution and arbitrary cumulative distribution function (CDF). This family is called Weibull Lindley general family of distributions (WLGFD). On this approach, we derive the Weibull Lindley Pareto distribution (WLPD). Several properties are included, PDF,CDF, moment generating function, hazard rate, reversed hazard function, odd function, quantile function, order statistics and moments are proved of the WLPD. An estimation procedure by the method of maximum likelihood, fisher matrix and a simulation are studied of WLPD. Finally, we give graph of PDF, CDF, mean squared error and bias at different values of parameters. [ABSTRACT FROM AUTHOR]

The total retail sales of goods and services in the US is modelled using generalized pareto distribution (GPD) model from Extreme Value Theory. The trend test which is Mann-Kendall (MK) suggests that retail sales data exhibit a non-stationarity. Thus, the non-stationary GPD with a linear dependence in time is proposed. The maximum likelihood estimation (MLE) method is used to estimate the parameters of GPD model. The return level of US annual retail sales for the next 20, 50 and 100 years are being calculated. Results showed that both stationary and non-stationary GPD produce the commendable results in fitting the data. The assessment on Q-Q plot suggest that GPD distribution provides a good fit to the annual retail sales data using MLE method. However, non-stationary GPD with time as a linear covariate does improve the model. This is supported by the goodness-of-fit test where the AIC, BIC and LRT conclude the non-stationary performed quite well compared to the stationary model. Consequently, the non-stationary GPD model is the most appropriate, comprising linear effect in the location of extremal behavior, but homogeneity in all other aspects. The return levels provided in this study could provide some useful information to the country where the government should focus more on the retail industry as the retail industry has high potential to be primary sector of the economy in the country. In addition, the government should be more creative in strategizing the marketing plan into a global market and building up the alternative way to increase the profits while coping the challenges during the pandemic period. [ABSTRACT FROM AUTHOR]

One of the few goals of statistical modeling is to see and analyze the probability of an event which can be represented with data. A probability distribution that is used for modeling data should have some abilities such as flexibility for modeling different kinds of data. Therefore, modeling data is of great importance. Furthermore, insurance companies also need to model data, which in this case is called modeling claim data. Modeling the claims distribution has its own challenge (e.g. skewed and heavy tailed) since most of the claim distributions are different from any classical distributions, therefore researchers are trying to find new models that can fit insurance data better. In this paper, a composite Exponential-Pareto distribution was proposed and introduced. This distribution is equal, but not equivalent to, an exponential density up to a certain threshold value, and a Pareto type-I density for the rest of the model. When being compared with the exponential distribution, the emerging density has a similar shape and a larger tail, and while being compared with the Pareto distribution, the emerging density has a smaller tail. A method to develop a composite distribution is called as composite parametric modeling, which introduced by Cooray and Ananda (2005). In this model, both the exponential distribution and the Pareto type-I distribution have the same weight. Based on the result, composite Exponential-Pareto distribution has some limitations, which are likely to severely diminish its potential for practical applications to real world insurance data. In order to address these issues, there are two different composite Exponential-Pareto distributions based on exponential and Pareto type-I distributions in order to address these concerns. These two different composite Exponential-Pareto distributions are based on the two-component mixture model introduced by Scollnik (2007). The first distribution, which is a reinterpreted composite Exponential-Pareto distribution from the first composite Exponential-Pareto distribution based on the two-component mixture model, has a fixed mixing weight. Meanwhile, the second distribution is a composite Exponential-Pareto distribution with a mixing weight that is not fixed so the distribution can be more flexible and can model different kinds of data. These three composite Exponential-Pareto distributions has k-th raw-moment that only defined for some k > 0. Therefore, this distribution can be categorized as a heavy-tail distribution. The result of this research is a composite distribution that could model a lot of data with characteristics such as unimodal, right-skewed, and heavy-tail because the composite distribution has similar characteristics. A data illustration was presented as a demonstration for how to implement the composite Exponential-Pareto distribution. [ABSTRACT FROM AUTHOR]

JAGS is an open-source package to analyze graphical model that is written with extensibility in mind. The runjags package includes many enhancements to JAGS, including a custom JAGS module that contains some additional distributions in the Pareto family. A very flexible set of statistical models based on the logarithm of an F variate, the standardized Fisher's z distribution, was introduced more than 90 years ago. However, the standardized Fisher's z distribution is not yet adaptive for modeling, since the mode cannot be shifted from the zero point. This paper introduces the Fisher's z distribution, i.e., the standardized Fisher's z distribution which added a location parameter µ and a scale parameter σ. The mode of the distribution lies in µ. In this paper, we provide step-by-step instructions on how to add Fisher's z distribution to the runjags package. In order to affirm the accuracy of our implementation, we ran a comprehensive numerical experiment, using linear regression model. We conduct a simulation study to investigate the model performance compared to the normal or Gaussian error regression (GER) model. The results show that the Fisher's z error regression (ZER) model outperforms the GER model. [ABSTRACT FROM AUTHOR]

Income inequality is a matter of concern for any society and an interesting discussion topic, particularly for developing countries, since high-income inequality could be detrimental to economic growth. In Malaysia, upper-income earners are classified as the T20 group. This study analyzes the demographic profile of members of the T20 group living in urban areas in Malaysia. The upper-income distribution is described using the Pareto model, and a robust and efficient estimator called the probability integral transform statistic estimator is utilized to estimate the shape parameter of this model. Thereafter, a Gini index and Lorenz curve are derived to analyze the severity of income inequality among T20 group members. [ABSTRACT FROM AUTHOR]

In this paper we investigate the problem of rigorous expression for Pareto principle if applied to standard distributions, which could be emanated from The Central Limit Theorem. Necessity of this consideration is generally conditioned by extensive employment of statistical methods to optimized classification tasks and minimal utility models construction. The equation for 80/20-like ratio calculation was derived in the universal form (independent from all parameters of the distribution) due to effective determination of the kurtosis. We established the exact ratio as 76/24, which one can find useful for applied statistical analysis of physical and financial systems. [ABSTRACT FROM AUTHOR]

The paper investigates probabilities for p-outside values. It shows that they are very appropriate new numerical characteristics for describing the tail of the cumulative distribution function of the corresponding random variable. They are invariant within the whole probabilistic type. They always exist. They outperform the role of the excess, and have more general applications than the index of regular variation. Their theoretical values in many particular cases, e.g. Pareto, Stable, Gamma, Log-Logistic, Frechet, some p-max-stable laws among others are calculated, and corresponding functions are plotted and compared. These characteristics allow us to find estimators of the tail of the distribution outside the range of the data. Therefore they can be useful in analyzing high quantiles and extremal values. [ABSTRACT FROM AUTHOR]

Probability distributions are uncountably many. The task for a general and useful their classification still has no satisfactory solution. Due to lack of information outside the range of the data the tails of the distribution should be described via many characteristics. Index of regular variation is a good characteristic, but it puts too many distributions with very different tail behavior in one and the same class. One can consider for example Stable(α) and Hill-horror(α) laws with one and the same fixed parameter α > 0. When analyzing the tail behavior of the observed distribution we need some characteristic which does not depend on the moments because in the most important cases of the heavy-tailed distributions theoretical moments do not exist and the corresponding empirical moments fluctuate too much. In this paper, we show that probabilities for different types of outside values can be very appropriate characteristics of the tails of the observed distribution. They do not depend on increasing affine transformations and do not need the existence of the moments. The idea origins from Tukey’s box plots, and allows us to obtain one and the same characteristic of the tail behavior of the observed distribution within the whole distributional type with respect to all increasing affine transformations. These characteristics answer the question: “At what extent we can observe “unexpected” values?”. [ABSTRACT FROM AUTHOR]

The reliability is derived for n-cascade system is considered for two cases. Where Strength-stress follows Pareto and Weibull distributions. The general expression for the reliability of an n-cascade system is obtained and the system reliability is computed numerically for different values and parameters. [ABSTRACT FROM AUTHOR]

There is a range of phenomena in continuous, global multi-objective optimization, that cannot occur in single-objective optimization. For instance, in some multi-objective optimization problems it is possible to follow continuous paths of gradients of straightforward weighted scalarization functions, starting from locally efficient solutions, in order to reach globally Pareto optimal solutions. This paper seeks to better characterize multimodal multi-objective landscapes and to better understand the transitions from local optima to global optima in simple, path-oriented search procedures. [ABSTRACT FROM AUTHOR]

This paper introduces the first objective space algorithm which can exactly find all supported and non-supported non-dominated solutions to a mixed-integer multi-objective linear program with an arbitrary number of objective functions. This algorithm is presented in three phases. First it builds up a super-set which contains the Pareto front. This super-set is then modified to not contain any intersecting polytopes. Once this is achieved, the algorithm efficiently calculates which portions of the super-set are not part of the Pareto front and removes them, leaving exactly the Pareto front. [ABSTRACT FROM AUTHOR]

In this talk we show that the boundary of the Pareto critical set of an unconstrained multiobjective optimization problem (MOP) consists of Pareto critical points of subproblems considering subsets of the objective functions. If the Pareto critical set is completely described by its boundary (e.g., if we have more objective functions than dimensions in the variable space), this can be used to solve the MOP by solving a number of MOPs with fewer objective functions. If this is not the case, the results can still give insight into the structure of the Pareto critical set. This technique is especially useful for efficiently solving many-objective optimization problems by breaking them down into MOPs with a reduced number of objective functions. For further details on this topic, we refer to [1]. [ABSTRACT FROM AUTHOR]

Searching over the Pareto front for the most preferred decision requires providing multiple Pareto optimal solutions to an instance of the general multiobjective optimization problem. This process, especially for large-scale problems can be time consuming and even can go over the resource (time, memory required) budget. In that case, lower and upper bounds are necessary to judge if the solutions derived thus far are acceptable approximations of the Pareto optimal ones. To this aim we provide lower and upper bounds for the general multiobjective optimization problem. This work generalizes our similar development valid for a special case. [ABSTRACT FROM AUTHOR]

We consider the problem of approximating the Pareto front for the optimization of two C² functions. An algorithm is described that is efficient in the sense that the number of function evaluations that are not on the Pareto front grows as the square of the logarithm of the number of function evaluations. [ABSTRACT FROM AUTHOR]

This paper aims is to model the extreme temperature using block maxima method and hence predict the return level of high temperature in a certain period. The GEV distribution used as the appropriate limiting distribution for extreme data based on block maxima approach. It was found that the maximum temperature for all block sizes had Frechet type distribution and the monthly and yearly maxima series had better fit to GEV distribution compared to quarterly and half yearly blocks. In general, the return level increase as the block size decrease. [ABSTRACT FROM AUTHOR]

This paper discusses extreme magnitudes of residual water levels and their probabilistic behaviors. The study area is situated in the west of Java Sea, NW of Java Island. The discussion relies on recent two decades' Sea Surface Height (SSH) from two offshore points of observation in the west of Java Sea and Water Level (WL) from a tide station in Tanjung Priok port of Jakarta. The dataset of SSH is obtained by satellite altimetry on 10-day basis observation, while WL is recorded on hourly basis. Residuals are extracted from SSH and WL by removing their mean values (i.e. Mean Sea Surface, Mean Sea Level) and the tide. They range within the order of sub-meters. These count already for at least one-third of the tidal amplitude in the region. To these residuals, their mean and extreme patterns are explored. The chances of positive residuals are at least tripled with respect to the negative ones. The nearshore point, i.e. Tanjung Priok, experiences a greater magnitude of residuals than those in the offshore area. Here, we apply Generalized Extreme Value (GEV) and Generalized Pareto Distribution (GPD) methods respectively for Block Maxima/Minima (BM) and Peak Over Threshold (POT) samplings of residuals. It is found that, the extreme positive and negative residuals at 100-year return period are within less than +1 m in Tanjung Priok and just less than half-meter in the offshore area. While higher residuals are observed during the East monsoon in the offshore area, Tanjung Priok experiences higher residuals during the West monsoon. This is thought due to the prevailing wave fields, which are governed by the monsoonal winds. [ABSTRACT FROM AUTHOR]

Generally, the analysis of PM10 concentrations use the conventional method of the Extreme Value Distribution (EVD). On the other hand, the Bayesian approach offers a more comprehensible framework which incorporates all the uncertainties in the prediction process using the conventional methods. This study was undertaken with the purpose of evaluating the performance of non-informative priors in the Bayesian approach to estimate the Generalized Extreme Value's (GEV) and Generalized Pareto Distribution's (GPD) parameters and to find a suitable model to predict the level of PM10 concentrations. The daily maximum records of PM10 from 2000 - 2012 for Shah Alam, Bukit Rambai and Seberang Jaya, Malaysia were used. These data were provided by the Department of Environment, Malaysia. The performance of each distribution was evaluated, and the least error measures and the highest accuracy measures was selected as the best distribution. The best estimators for PM10 concentrations was the GEV and it could be applied in the PM10 analysis to predict high concentrations of PM10 in these stations. [ABSTRACT FROM AUTHOR]

Most real life data sets are non-stationary, where they are affected by covariates. The conventional method of modelling non-stationary extremes are by setting a constant high threshold, where the threshold exceedances are modelled by Generalized Pareto distribution (GPD) and covariates model is incorporated in the GPD parameters to account for the non-stationarity. However, the asymptotic basis of the GPD model might be violated, where threshold might be high enough for GPD approximation on certain covariates but not on others. In this paper, a covariate-varying threshold selection method based on regression tree is proposed and applied on simulated non-stationary data sets. The tree is used to partition data sets into homogenous groups with similar covariate condition. The uncertainty associated with this threshold selection method is evaluated using the bootstrap procedure. The bootstrap percentile interval obtained is not too wide which conclude that the uncertainty caused by the threshold choice is not too big. Besides, the exceedances of the tree-based threshold can be modelled by stationary GPD model which is simpler than non-stationary model. [ABSTRACT FROM AUTHOR]

The class of L ∩ D is generated by intersection of two important subclasses of heavy tailed distributions: The long tailed distributions and dominated varying distributions. This class itself is also an important member of heavy tailed distributions and has some principal application areas especially in renewal, renewal reward and random walk processes. The aim of this study is to observe some well and less known results on renewal functions generated by the class of L ∩ D and apply them into a special renewal reward process which is known in the literature a semi Markovian inventory model of type (s, S). Especially we focused on Pareto distribution which belongs to the L ∩ D subclass of heavy tailed distributions. As a first step we obtained asymptotic results for renewal function generated by Pareto distribution from the class of L ∩ D using some well-known results by Embrechts and Omey [1]. Then we applied the results we obtained for Pareto distribution to renewal reward processes. As an application we investigate inventory model of type (s, S) when demands have Pareto distribution from the class of L ∩ D. We obtained asymptotic expansion for ergodic distribution function and finally we reached asymptotic expansion for nth order moments of distribution of this process. [ABSTRACT FROM AUTHOR]

Modelling of snow exceedances is of great importance and interest for ecology, civil engineering and general public. We suggest the favorable fit for exceedances related to the exceptional snow loads from Slovakia, assuming that the data is driven by Generalised Pareto Distribution or Generalized Extreme Value Distribution. Further, the statistical dependence between the maximal snow loads and the corresponding altitudes is studied. [ABSTRACT FROM AUTHOR]

We can observe self-organized networks all around us. These networks are, in general, scale invariant networks described by the Bianconi-Barabasi model. The self-organized networks (networks formed naturally when feedback acts on the system) show certain universality. These networks, in simplified models, have scale invariant distribution (Pareto distribution type I) and parameter α has value between 2 and 5. The textbooks are extremely important in the learning process and from this reason we studied physics textbook at the level of sentences and physics terms (bipartite network). The nodes represent physics terms, sentences, and pictures, tables, connected by links (by physics terms and transitional words and transitional phrases). We suppose that learning process are more robust and goes faster and easier if the physics textbook has a structure similar to structures of self-organized networks. [ABSTRACT FROM AUTHOR]

Extreme flood event are among environmental events with the most disastrous consequences for human society. This paper deals with the identification of homogeneous regions through important steps in the regional frequency analysis. Streamflow totals measured at 70 stations over 1960-2009. The cluster analysis uses kriging technique and shows three regions of streamflow in Peninsular Malaysia. The homogeneity test of L-moments shows that some of these regions are homogeneous. Using the goodness-of-fit test, Z-Dist, the regional frequency distribution functions for each group are then selected. In this study, five three parameter distributions generalized logistic (GLO), generalized extreme-value (GEV), generalized pareto distributions (GPA), Pearson Type III (P3), and three parameter Lognormal (LN3) were fitted to the three homogeneous regions. [ABSTRACT FROM AUTHOR]

Indonesia has tropical climate with small variation of temperature but quite large variation of rainfall. So the rainfall which is an essential climate element related to climate change has to be observed. Climate change may increase the incidence of extreme rainfall that affects flooding in farmland. In order to anticipate the occurrence of extreme rainfall, the information of rainfall forecast is required. Statistical Downscaling (SD) is a technique to model the relationship between global scale data and local scale data. Global Circulation Model (GCM) output is global scale data and rainfall is local scale data. GCM has characteristic non-linear, high dimension, and multicolinierity. These problem can be overcome by principal component analysis (PCA). One of the primary methods for estimating extreme rainfall is generalize Pareto distribution (GPD) regression based on a threshold. The objective of this study is SD modeling based on GPD to predict extreme rainfall. The result show that GPD models can predict extreme rainfall well. Monthly rainfall prediction in January and December show a higher value than the actual data, but predictions follow actual data pettern well, especially during extreme rainfall. February has the highest rainfall that occurred in 2008 with a value of 439 mm/month. This value can be estimated either by prediction on quantile 0.95. [ABSTRACT FROM AUTHOR]

Rainfall pattern are good indicators for potential disasters. Global Circulation Model (GCM) contains global scale information that can be used to predict the rainfall data. Statistical downscaling (SD) utilizes the global scale information to make inferences in the local scale. Essentially, SD can be used to predict local scale variables based on global scale variables. SD requires a method to accommodate non linear effects and extreme values. Extreme value Theory (EVT) can be used to analyze the extreme value. One of methods to identify the extreme events is peak over threshold that follows Generalized Pareto Distribution (GPD). The vector generalized additive model (VGAM) is an extension of the generalized additive model. It is able to accommodate linear or nonlinear effects by involving more than one additive predictors. The advantage of VGAM is to handle multi response models. The key idea of VGAM are iteratively reweighted least square for maximum likelihood estimation, penalized smoothing, fisher scoring and additive models. This works aims to analyze extreme rainfall data in Indramayu using VGAM. The results show that the VGAM with GPD is able to predict extreme rainfall data accurately. The prediction in February is very close to the actual value at quantile 75. [ABSTRACT FROM AUTHOR]

The Pareto distribution is a well known and important model in Statistics. It has been used to study large incomes, city population size, size of losses, stock price fluctuations, number of citations received by papers and other similar phenomena. In this work we compare the finite sample performance of several estimation methods, namely the Moment, Maximum Likelihood and Quantile Regression methods. The comparison will be made through a Monte-Carlo simulation study. [ABSTRACT FROM AUTHOR]

Ranked set sampling (RSS) is recognized as a useful sampling scheme for improving the precision of the parameter estimates and increasing the efficiency of estimation. This type of scheme is appropriate when the variable of interest is expensive or time consuming to be quantified, but easy and cheap to be ranked. In this study, the estimation of the shape parameter of the Pareto distribution of the first type when the scale is known is studied for the data that are gathered under simple random sampling (SRS), RSS, and selective order statistics based on the maximum (SORSS(max)). The confidence intervals for the shape parameter of Pareto distribution under the sampling techniques considered are determined. A simulation study is carried out to compare the confidence intervals in terms of coverage probabilities (CPs) and expected lengths (ELs). When the coverage probabilities and expected lengths for the confidence intervals of the shape parameter of Pareto distribution determined based on the different sampling methods are compared, the coverage probabilities and expected lengths are found to be more precise under RSS as opposed to SRS. In particular, it is found that the coverage probabilities under SORSS(max) is closest to the nominal value of 0.95. [ABSTRACT FROM AUTHOR]

The high particulate matter (PM10) level is the prominent issue causing various impacts to human health and seriously affecting the economics. The asymptotic theory of extreme value is apply for analyzing the relation of extreme PM10data from two nearby air quality monitoring stations. The series of daily maxima PM10 for Johor Bahru and Pasir Gudang stations are consider for year 2001 to 2010databases. The 85% and 95% marginal quantile apply to determine the threshold values and hence construct the series of exceedances over the chosen threshold. The logistic, asymmetric logistic, negative logistic and asymmetric negative logistic models areconsidered as the dependence function to the joint distribution of a bivariate observation. Maximum likelihood estimation is employed for parameter estimations. The best fitted model is chosen based on the Akaike Information Criterion and the quantile plots. It is found that the asymmetric logistic model gives the best fitted model for bivariate extreme PM10 data and shows the weak dependence between two stations. [ABSTRACT FROM AUTHOR]

The objective of this study is to investigate the suitable probability distribution to model the extreme share returns in Malaysia. To achieve this, weekly and monthly maximum daily share returns are derived from share prices data obtained from Bursa Malaysia over the period of 2000 to 2012. The study starts with summary statistics of the data which will provide a clue on the likely candidates for the best fitting distribution. Next, the suitability of six extreme value distributions, namely the Gumbel, Generalized Extreme Value (GEV), Generalized Logistic (GLO) and Generalized Pareto (GPA), the Lognormal (GNO) and the Pearson (PE3) distributions are evaluated. The method of L-moments is used in parameter estimation. Based on several goodness of fit tests and L-moment diagram test, the Generalized Pareto distribution and the Pearson distribution are found to be the best fitted distribution to represent the weekly and monthly maximum share returns in Malaysia stock market during the studied period, respectively. [ABSTRACT FROM AUTHOR]

This study aims to examine the presence of outliers in the upper tail of Malaysian income distribution under the assumption that the data follow Pareto model. For this purpose, three types of boxplot: standard boxplot, adjusted boxplot and generalized boxplot are considered. The performance of these boxplots is determined by a simulation study. In this study, the data were simulated from Pareto distribution, P(1, α = 2, 3, 4), then the simulated data were contaminated by replacing a proportion ε (3%, 5%, 10%) of randomly selected data. It is found that the generalized boxplot gives higher power value compared to the standard and adjusted boxplots. Therefore, the generalized boxplot was used for determining the presence of outliers in the upper tail of income distribution, while the threshold for Pareto tail modelling was determined by using Van Kerm’s formula. The results showed that 0.4%, 0.4%, 0.9% and 1.2% outliers were detected by the generalized boxplot in the household income data that exceeded the threshold for the years of 2007, 2009, 2012 and 2014. [ABSTRACT FROM AUTHOR]

In the satellite navigation community, error overbound has been implemented in the process of integrity monitoring. In this work, MATLAB programming is used to implement the overbounding of satellite positioning error CDF. Using a trajectory of reference, the horizontal position errors (HPE) are computed and its non-parametric distribution function is given by the empirical Cumulative Distribution Function (ECDF). According to the results, these errors have a heavy-tailed distribution. Sınce the ECDF of the HPE in urban environment is not Gaussian distributed, the ECDF is overbound with the CDF of the generalized Pareto distribution (GPD). [ABSTRACT FROM AUTHOR]