L-Moments and TL-Moments as an Alternative Tool of Statistical Data Analysis

Bílková, Diana

doi:10.4236/jamp.2014.210104

Cited by 10 publications

(3 citation statements)

References 5 publications

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“…The formula is used in the DWA model as well as for the GEV. The distribution parameters are estimated using the L-moment method recommended by Hosking (1990) or Bílková (2014). This provides robust results for small samples with statistical outliers (extreme values).…”

Section: Precipitation Statisticsmentioning

confidence: 99%

Regional analysis of convective heavy rain events in the German State of Hesse

Perschke,

Schmalz,

Ruiz Rodriguez

2023

Preprint

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Abstract. The convective heavy precipitation events, which occur primarily in the summer months, cannot be recorded representatively by ground-based precipitation stations due to their frequently small spatial extent, short life span and high rapidly changing intensity. The radar network of the German Weather Service, on the other hand, records area-wide, spatiotemporally highly resolved precipitation information that enables comprehensive identification of precipitation objects. In this study, a method for the identification, description and classification of convective precipitation objects considering a flood-relevant event extent is presented. Assuming an orographic independence of the events in the Central European low mountain range, the German State of Hesse is chosen as representative study area. Considering the spatial and temporal extent of the identified events, the most extreme expression is selected and independence is ensured. With the assignment of an authoritative duration for the intensive main rainfall phase, an extensive collection of heavy precipitation objects results. The results show a characteristic event length of 15 to 60 minutes; longer durations are underrepresented and exhibit inhomogeneous extreme value behavior. Statistically, the generated samples can be well represented and classified by the generalized extreme value distribution. The evaluation allows us to make a regional characterization of convective heavy precipitation.

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Section: Precipitation Statisticsmentioning

confidence: 99%

Regional analysis of convective heavy rain events in the German State of Hesse

Perschke,

Schmalz,

Ruiz Rodriguez

2023

Preprint

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“…The method of L-moments was discussed from various earlier studies by Hosking (1990) who provided guidelines for the practical use of L-moments. Hosking (1990Hosking ( , 1992Hosking ( , 1994Hosking ( , 2006, Hosking and Wallis (1995), Sillitto (1969), Elamir andSeheult (2001, 2004), Jones (2004), Asquith (2007), Abdul-Moniem (2007), Karvanen (2006), Bílková (2014) and Dutang (2016) considered various theoretical aspects and applications of L-moments for complete data.…”

Section: -L-moments Via Ppwm For Censored Data Formentioning

confidence: 99%

Comparison of Direct L-moments, L-moments and ML Estimation Methods for Weibull Distribution with Type-I Censoring

El-Kelany¹,

Ibrahim²

2019

المجلة العلمیة لقطاع کلیات التجارة

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This paper presents a comparison of three different methods, Direct Lmoments, L-moments via partial probability-weighted moments (PPWM) and maximum likelihood (ML) methods, respectively, to estimate the two parameters of Weibull distribution with Type-I censored data. These methods are compared in terms of estimate of the unknown parameters, relative bias and root of mean square error (RMSE) using Monte Carlo simulation to select the best method. Also, a real data set is considered to achieve the results.

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“…where B * ( , ; z) is "the upper beta function at z" given by (9). Now expand (1 − w) c−1 in the integral of ( 15), using the binomial series expansion, Abramowitz and Stegun [3] p.14, to get that;…”

mentioning

confidence: 99%

A Generalized Modification of the Kumaraswamy Distribution for Modeling and Analyzing Real-Life Data

Alshkaki¹

2020

Stat., optim. inf. comput.

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In this paper, a generalized modification of the Kumaraswamy distribution is proposed, and its distributional and characterizing properties are studied. This distribution is closed under scaling and exponentiation, and has some well-known distributions as special cases, such as the generalized uniform, triangular, beta, power function, Minimax, and some other Kumaraswamy related distributions. Moment generating function, Lorenz and Bonferroni curves, with its moments consisting of the mean, variance, moments about the origin, harmonic, incomplete, probability weighted, L, and trimmed L moments, are derived. The maximum likelihood estimation method is used for estimating its parameters and applied to six different simulated data sets of this distribution, in order to check the performance of the estimation method through the estimated parameters mean squares errors computed from the different simulated sample sizes. Finally, four real-life data sets are used to illustrate the usefulness and the flexibility of this distribution in application to real-life data.

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L-Moments and TL-Moments as an Alternative Tool of Statistical Data Analysis

Cited by 10 publications

References 5 publications

Regional analysis of convective heavy rain events in the German State of Hesse

Regional analysis of convective heavy rain events in the German State of Hesse

Comparison of Direct L-moments, L-moments and ML Estimation Methods for Weibull Distribution with Type-I Censoring

A Generalized Modification of the Kumaraswamy Distribution for Modeling and Analyzing Real-Life Data

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