An efficient estimator of the parameters of the generalized lambda distribution

Dedduwakumara, Dilanka S.; Prendergast, Luke A.; Staudte, Robert G.

doi:10.1080/00949655.2020.1808979

Cited by 6 publications

(5 citation statements)

References 32 publications

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“…As demonstrated in the plot of robust moments (Figure 5) GLD remains one of the most flexible unbounded distributions, capable of accommodating a wide range of shapes. Dedduwakumara et al (2021) described a two-step method for fitting FKML GLD using the probability density quantile function (Staudte, 2017). However, when applying their method to fitting the CSW GLD, the second step becomes unnecessary as the location and scale can be directly mapped to the empirical first and second robust moments.…”

Section: Discussionmentioning

confidence: 99%

“…Recently, Dedduwakumara et al (2021) proposed a new method of matching the shape of the GLD distribution to data using the probability density quantile (pdQ) function (Staudte, 2017). For the quantile function Q(v), v ∈ [0, 1] and the corresponding density quantile function f (Q(v)) = [q(v)] −1 , the pdQ is defined as…”

Section: Generalized Lambda Distributionmentioning

confidence: 99%

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Quantile-parameterized distributions for expert knowledge elicitation

Perepolkin,

Lindsröm,

Sahlin

2023

Preprint

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This paper presents a comprehensive overview of quantile-parameterized distributions (QPDs) as a powerful tool for capturing expert predictions and parametric judgments. We survey various types of QPDs covered in the literature and focus on the Myerson distribution as the simplest method of parameterizing a distribution by a set of quantile-probability pairs. We propose the generalization of the Myerson distribution to increase the flexibility of its tails. Additionally, we explore the extension of QPDs to the multivariate setting, discussing methods for constructing bivariate distributions with quantile-parameterized margins.

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Section: Discussionmentioning

confidence: 99%

Section: Generalized Lambda Distributionmentioning

confidence: 99%

Quantile-parameterized distributions for expert knowledge elicitation

Perepolkin,

Lindsröm,

Sahlin

2023

Preprint

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“…Today the research area of quantile distributions is an active field of interest for many scientists. The most popular quantile distributions covered in the literature are generalized g-and-h and its sibling g-and-k distribution (Haynes and Mengersen, 2005;Jacob, 2017;Prangle, 2017;Rayner and MacGillivray, 2002), Generalized Lambda Distribution, known as GLD (Aldeni et al, 2017;Chalabi et al, 2012;Dedduwakumara et al, 2021;Fournier et al, 2007;Freimer et al, 1988), Wakeby distribution (Rahman et al, 2015) and Govindarajulu distribution (Nair et al, 2012(Nair et al, , 2013. Although in this paper we focus on the parametric quantile distributions, the quantile distributions parameterized by the quantile-probability pairs ("quantile-parametrized" quantile distributions) are also worth a mention.…”

Section: Quantile Distributionsmentioning

confidence: 99%

The tenets of quantile-based inference in Bayesian models

Perepolkin¹,

Goodrich²,

Sahlin³

2021

Preprint

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This paper extends the application of Bayesian inference to probability distributions defined in terms of its quantile function. We describe the method of *indirect likelihood* to be used in the Bayesian models with sampling distributions which lack an explicit cumulative distribution function. We provide examples and demonstrate the equivalence of the "quantile-based" (indirect) likelihood to the conventional "density-defined" (direct) likelihood. We consider practical aspects of the numerical inversion of quantile function by root-finding required by the indirect likelihood method. In particular, we consider a problem of ensuring the validity of an arbitrary quantile function with the help of Chebyshev polynomials and provide useful tips and implementation of these algorithms in Stan and R. We also extend the same method to propose the definition of an *indirect prior* and discuss the situations where it can be useful

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“…Figure 1 illustrates that GLD estimates the quantile function well, where the parameter of GLD is obtained by Dedduwakumara et al . (2021). We refer the reader to Karian and Dudewicz (2000) for a complete list of distributions that the GLD can represent and their corresponding parameters.…”

Section: Introductionmentioning

confidence: 99%

Non‐crossing quantile double‐autoregression for the analysis of streaming time series data

Jiang,

Kai Choy,

2023

Journal Time Series Analysis

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Many financial time series not only have varying structures at different quantile levels and exhibit the phenomenon of conditional heteroscedasticity at the same time but also arrive in the stream. Quantile double‐autoregression is very useful for time series analysis but faces challenges with model fitting of streaming data sets when estimating other quantiles in subsequent batches. This article proposes a renewable estimation method for quantile double‐autoregression analysis of streaming time series data due to its ability to break with storage barrier and computational barrier. Moreover, the proposed flexible parametric structure of the quantile function enables us to predict any interested quantile value without quantile curve crossing problem or keeping the desirable monotone property of the conditional quantile function. The proposed methods are illustrated using current data and the summary statistics of historical data. Theoretically, the proposed statistic is shown to have the same asymptotic distribution as the standard version computed on an entire data stream with the data batches pooled into one data set, without additional condition. Simulation studies and an empirical example are presented to illustrate the finite sample performance of the proposed methods.

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An efficient estimator of the parameters of the generalized lambda distribution

Cited by 6 publications

References 32 publications

Quantile-parameterized distributions for expert knowledge elicitation

Quantile-parameterized distributions for expert knowledge elicitation

The tenets of quantile-based inference in Bayesian models

Non‐crossing quantile double‐autoregression for the analysis of streaming time series data

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