Extreme value prediction via a quantile function model

In this talk, we introduce a newly developed quantile function model that can be used for estimating conditional distributions of financial returns and for obtaining multi-step ahead out-of-sample predictive distributions of financial returns. Since we forecast the whole conditional distributions, any predictive quantity of interest about the future financial returns can be obtained simply as a by-product of the method. We also show an application of the model to the daily closing prices of Dow Jones Industrial Average (DJIA) series over the period from 2 January 2004 - 8 October 2010. We obtained the predictive distributions up to 15 days ahead for the DJIA returns, which were further compared with the actually observed returns and those predicted from an AR-GARCH model. The results show that the new model can capture the main features of financial returns and provide a better fitted model together with improved mean forecasts compared with conventional methods. We hope this talk will help audience to see that this new model has the potential to be very useful in practice.

FORTRAN 77 program for constructing and plotting confidence bands for the distribution and quantile functions for truncated data

The odd exponentiated Rayleigh-G family: A flexible statistical framework for reliability and radiation modeling

In this article, we introduce a new one-parameter model, which is named sine inverted exponential (SIE) distribution. The SIE distribution is a new extension of the inverse exponential (IE) distribution. The SIE distribution aims to provide the SIE model for data-fitting purposes. The SIE distribution is more flexible than the inverted exponential (IE) model, and it has many applications in physics, medicine, engineering, nanophysics, and nanoscience. The density function (PDFu) of SIE distribution can be unimodel shape and right skewed shape. The hazard rate function (HRFu) of SIE distribution can be J-shaped and increasing shaped. We investigated some fundamental statistical properties such as quantile function (QFu), moments (Mo), moment generating function (MGFu), incomplete moments (ICMo), conditional moments (CMo), and the SIE distribution parameters were estimated using the maximum likelihood (ML) method for estimation under censored samples (CS). Finally, the numerical results were investigated to evaluate the flexibility of the new model. The SIE distribution and the IE distribution are compared using two real datasets. The numerical results show the superiority of the SIE distribution.

In this work, we provide an extended one parameter distribution into a new two parameter life model and called it the New Extended “A” (NEA) distribution. This new model provides the best description of the data sets in different sectors. Both of the probability distribution function (PDF) and the cumulative distribution function (CDF) of the NEA distribution are derived from one of the new families. The suggested distribution’s properties including moments, quantile function, survival function, hazard rate function, odds function and mode are deduced and acquired in explicit forms using Taylor expansion to simplify the integrals. The Rényi entropy of NEA distribution is derived and the maximum likelihood method for estimating its parameters is deduced. Numerical simulations are used to study the behavior of the parameters with different sizes of samples. According to the simulation results of this work, the maximum likelihood estimators are advised to be a suitable estimation method for estimating the parameters of the NEA distribution. We show the importance and flexibility of the NEA distribution by comparing it to some competing distributions using five real data sets from different sectors in behavioral sciences, ecophysiological, industry and health. Our new model is shown to be better than all competing distributions. Received: October 6, 2023Accepted: November 15, 2023

In this article, a new generalization of the Topp-Leone distribution with a unit interval, namely Mixed Topp-Leone-Kumaraswamy distribution is defined and studied. The mathematical properties of this mixing distribution are described. Moments, quantile function, R?nyi entropy, incomplete moments and moments of residual are obtained for the new Mixed Topp-Leone - Kumaraswamy distribution. The maximum likelihood (MLE), Crans (CM) , Percentile (PM) and Particle Swarm Optimization(PSO) estimators of the parameters are derived. The percentile Method is more efficient method as compred to the others. Two real data sets are used to illustrate an application and superiority of the proposed distribution.

To generate random variates from an unknown continuous distribution via the inverse transform method, we present a flexible, computationally tractable procedure for estimating the associated inverse distribution function based on sample data. Previously proposed methods for estimating inverse distribution functions can fail in either the distribution-fitting or variate-generation stages of application. To avoid these difficulties, we have developed the procedure IDPF for estimating an Inverse Distribution with a Polynomial Filter. After a first-cut or reference distribution has been obtained by some standard technique, a front-end polynomial filter for the inverse of the reference distribution is estimated by constrained nonlinear regression so that the resulting inverse distribution has minimum distance from the empirical inverse distribution. The constraints on the regression ensure that the fitted inverse distribution function is nondefective and monotonically nondecreasing. A specific implementation of this procedure is based on well-known techniques for obtaining a reference fit from the Johnson translation system of distributions. We present the results of a Monte Carlo study to demonstrate the effectiveness of the method. Compared to the reference fit, procedure IDPF yields significantly better approximations not only to the empirical inverse distribution function but also to the underlying theoretical inverse distribution function.

Let {Xn, n ≥ 1} be a sequence of stationary non-negative associated random variables with common marginal distribution function F(x) and quantile function Q(u), where Q(u) is defined as F(Q(u)) = u. Here we consider the smooth estimation of Q(u), adapted from generalized kernel smoothing (Cheng and Parzen J. Stat. Plann. Infer. 59, 291–307, 1997) of the empirical quantile function. Some asymptotic properties of the kernel quantile estimator, for associated sequences, are also established parallel to those in the i.i.d. case. Various estimators in this class of estimators are contrasted, through a simulation study, among themselves and with an indirect smooth quantile estimator obtained by inverting the Poisson weights based estimator of the distribution function studied in Chaubey et al. (Statist. Probab. Lett. 81, 267–276, 2011). The indirect smoothing estimator seems to be the best estimator on account of smaller MSE, however, a quantile estimator based on the Bernstein polynomials and that using the corrected Poisson weights turn out to be almost as good as the inverse distribution function estimator using Poisson weights.

This work is devoted to the study of rates of convergence of the empirical measures μ n = 1 n ∑ k = 1 n δ X k \mu _n = \frac {1}{n} \sum _{k=1}^n \delta _{X_k} , n ≥ 1 n \geq 1 , over a sample ( X k ) k ≥ 1 {(X_k)}_{k \geq 1} of independent identically distributed real-valued random variables towards the common distribution μ \mu in Kantorovich transport distances W p W_p . The focus is on finite range bounds on the expected Kantorovich distances E ( W p ( μ n , μ ) ) \mathbb {E}(W_p(\mu _n,\mu )) or [ E ( W p p ( μ n , μ ) ) ] 1 / p \big [ \mathbb {E}(W_p^p(\mu _n,\mu )) \big ]^{1/p} in terms of moments and analytic conditions on the measure μ \mu and its distribution function. The study describes a variety of rates, from the standard one 1 n \frac {1}{\sqrt n} to slower rates, and both lower and upper-bounds on E ( W p ( μ n , μ ) ) \mathbb {E}(W_p(\mu _n,\mu )) for fixed n n in various instances. Order statistics, reduction to uniform samples and analysis of beta distributions, inverse distribution functions, log-concavity are main tools in the investigation. Two detailed appendices collect classical and some new facts on inverse distribution functions and beta distributions and their densities necessary to the investigation.

In this work, we introduce a novel generalization of the extended exponential distribution with four parameters through the Kumaraswamy family. The proposed model is referred to as the Kumaraswamy extended exponential (KwEE). The significance of the suggested distribution from its flexibility in applications and data modeling. As specific sub-models, it includes the exponential, Kumaraswamy exponential, Kumaraswamy Lindley, Lindley, extended exponential, exponentiated Lindley, gamma and generalized exponential distributions. The representation of the density function, quantile function, ordinary and incomplete moments, generating function, and reliability of the KwEE distribution are all derived. The maximum likelihood approach is used to estimate model parameters. A simulation study for maximum likelihood estimates was used to investigate the behaviour of the model parameters. A numerical analysis is performed for various sample sizes and parameter values to analyze the behaviour of estimates using accuracy measures. According to a simulated investigation, the KwEE's maximum likelihood estimates perform well with increased sample size. We provide two real-world examples utilizing applied research to demonstrate that the new model is more effective.

Intensity-duration-frequency relationship of WBGT extremes using regional frequency analysis in South Korea

This article proposes various nonparametric tools based on measure transportation for directional data. We use optimal transports to define new notions of distribution and quantile functions on the hypersphere, with meaningful quantile contours and regions and closed-form formulas under the classical assumption of rotational symmetry. The empirical versions of our distribution functions enjoy the expected Glivenko–Cantelli property of traditional distribution functions. They provide fully distribution-free concepts of ranks and signs and define data-driven systems of (curvilinear) parallels and (hyper)meridians. Based on this, we also construct a universally consistent test of uniformity and a class of fully distribution-free and universally consistent tests for directional MANOVA which, in simulations, outperform all their existing competitors. A real-data example involving the analysis of sunspots concludes the article.

In order to reduce the cost of corrections and time needed for the block assembly process, the reverse setting method is applied for a back-heated block to neutralize deck deformation. The proper reverse setting shape for a back-heated block to correct deformation improved the deck flatness, but an excessive amount of reverse setting could inversely affect the flatness of the block. A prediction method was developed for the proper reverse setting shape using a back-heated block, considering the complex geometry of blocks, thickness of the deck plate, and thermal loading conditions such as welding and back-heating. The prediction method was developed by combining the re-meshing technique and inherent strain-based deformation analysis using the finite element method. Because the flatness deviation was decreased until the lower critical point and thereafter it tended to increase again, the optimum value for which the flatness was the best case was selected by repeatedly calculating the predefined reverse setting values. Based on this analysis and the study of the back-heating deformation of large assembly blocks, including the reverse setting shape, the mechanism for selecting the optimum reverse setting value was identified. The developed method was applied to the actual blocks of a ship, and it was confirmed that the flatness of the block was improved. It is concluded that the developed prediction method can be used to predict the optimum reverse setting shape value of a ship’s block, which will reduce the cost of corrections in the construction stage.

Norm-based inequality measures are developed within the unequally distributed/relative unequally distributed (UD/RUD) framework by applying the L1 norm and the squared L2 norm to the cumulative distribution and quantile function (CDQF), the quantile function (QF), and their combined representation. All six indices maintain key properties such as scale, replication, and translation invariance, as well as anonymity, and their behavior under Pigou-Dalton transfers and subgroup decomposition is examined analytically. The indices based on the cumulative distribution and quantile function combine the vertical and horizontal gaps, giving them representation decomposability and making them the most informative overall measures of inequality. A Monte Carlo study on six contrasting income distributions corroborates these theoretical advantages, confirming finite, stable values even for mixed-sign and heavy-tailed supports.

ABSTRACTRecently, in the literature, the use of quantile functions in the place of distribution functions has provided new models, alternative methodology and easier algebraic manipulations. In this paper, we introduce new orders among the random variables in terms of their quantile functions like the reversed hazard quantile function, the reversed mean residual quantile function and the reversed variance residual quantile function orders. The relationships among the proposed orders and some existing orders are also discussed.