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QDistributions.bib
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@techreport{chalabi2012FlexibleDistributionModeling,
address = {Zurich, Switzerland},
type = {Working paper},
title = {Flexible distribution modeling with the generalized lambda distribution},
url = {https://mpra.ub.uni-muenchen.de/43333/},
abstract = {We investigate the generalized lambda distribution with infinite support
as an alternative distribution for modeling financial return series with power
law tails. We derive expressions for the distribution, for random number
generation, and for financial risk measures including value at risk, expected
shortfall and tail indices. We introduce a new robust moment approach for
the estimation of the distribution parameters based on the median, inter-
quartile range, Bowley’s skewness and Moors’ kurtosis. In addition using a
Monte Carlo approach we explore the use of several estimation approaches
including maximum log likelihood, maximum product spacing, goodness of
fit testing, and histogram binning. A new four-parameter parameterization
allows an intuitive interpretation based on the asymmetry and the tail be-
haviour of the distribution. We also introduce a new method of obtaining
parameter estimates in which the data is standardized to have zero median
and unit interquartile range and then a generalized lambda distribution with
zero median and unit interquartile range is fitted to the data. This reduces
the number of parameters to two allowing for more efficient parameter esti
mation.},
number = {MPRA Paper No. 43333,},
institution = {ETH},
author = {Chalabi, Yohan and Scott, David J and Wuertz, Diethelm},
month = dec,
year = {2012},
note = {tex.ids= chalabi2012FlexibleDistributionModelinga},
keywords = {No DOI found},
file = {chalabi_2012_flexible_distribution_modeling_with_the_generalized_lambda_distribution.pdf:/home/dm0737pe/MEGA/ZoteroLibrary/chalabi_2012_flexible_distribution_modeling_with_the_generalized_lambda_distribution.pdf:application/pdf},
}
@article{chakrabarty2021GeneralizationQuantileBasedFlattened,
title = {A {Generalization} of the {Quantile}-{Based} {Flattened} {Logistic} {Distribution}},
volume = {8},
issn = {2198-5812},
url = {https://doi.org/10.1007/s40745-021-00322-3},
doi = {10.1007/s40745-021-00322-3},
abstract = {In this paper, we propose a generalization of the quantile-based flattened logistic distribution Sharma and Chakrabarty (Commun Stat Theory Methods 48(14):3643–3662, 2019. https://doi.org/10.1080/03610926.2018.1481966). Having described the need for such a generalization from the data science perspective, several important properties of the distribution are derived here. We show that the rth order L-moment of the distribution can be written in a closed form expression. The L-skewness ratio and the L-kurtosis ratio of the distribution have been studied in detail. The distribution is shown to posses a skewness-invariant kurtosis measure based on quantiles and L-moments. The method of matching L-moments estimation has been used to estimate the parameters of the proposed model. The model has been applied to two real-life datasets and appropriate goodness-of-fit procedures have been used to test the validity of the model.},
language = {en},
number = {3},
urldate = {2022-09-29},
journal = {Annals of Data Science},
author = {Chakrabarty, Tapan Kumar and Sharma, Dreamlee},
month = sep,
year = {2021},
keywords = {Quantile function, Asymptotic variance, L-moment, order statistics, Flattened generalized logistic distribution, Skewness-invariant kurtosis},
pages = {603--627},
file = {chakrabarty_sharma_2021_a_generalization_of_the_quantile-based_flattened_logistic_distribution.pdf:/home/dm0737pe/MEGA/ZoteroLibrary/chakrabarty_sharma_2021_a_generalization_of_the_quantile-based_flattened_logistic_distribution.pdf:application/pdf},
}
@inproceedings{chakrabarty2018QuantileBasedSkewLogistic,
address = {Singapore},
series = {Springer {Proceedings} in {Mathematics} \& {Statistics}},
title = {The {Quantile}-{Based} {Skew} {Logistic} {Distribution} with {Applications}},
isbn = {9789811312236},
doi = {10.1007/978-981-13-1223-6_6},
abstract = {In this paper, a modified form of the quantile based skew logistic distribution of Van Staden and King (Stat Probab Lett, 96:109–116, 2015) originally introduced by Gilchrist (Statistical modelling with quantile functions. CRC Press, 2000) has been studied. Some classical and quantile based properties of the distribution have been obtained. L-moments and L-ratios of the distribution have been obtained in closed form. The nature of L-Skewness and L-kurtosis of the distribution have been studied in detail. A brief study on the order statistics of the distribution has been done. The estimation of parameters of the proposed model is approached by the methods of matching L-moments estimation. Finally, we apply the proposed model to real datasets and compare the fit with the quantile based skew logistic distribution of Van Staden and King (Stat Probab Lett, 96:109–116, 2015).},
language = {en},
booktitle = {Statistics and its {Applications}},
publisher = {Springer},
author = {Chakrabarty, Tapan Kumar and Sharma, Dreamlee},
editor = {Chattopadhyay, Asis Kumar and Chattopadhyay, Gaurangadeb},
year = {2018},
keywords = {Order statistics, Quantile function, Asymptotic variance, L-moment, Flattened skew logistic distribution},
pages = {51--73},
file = {chakrabarty_sharma_2018_the_quantile-based_skew_logistic_distribution_with_applications.pdf:/home/dm0737pe/MEGA/ZoteroLibrary/chakrabarty_sharma_2018_the_quantile-based_skew_logistic_distribution_with_applications.pdf:application/pdf},
}
@book{gilchrist2000StatisticalModellingQuantile,
address = {Boca Raton},
title = {Statistical modelling with quantile functions},
isbn = {978-1-58488-174-2},
url = {https://doi.org/10.1201/9781420035919},
publisher = {Chapman \& Hall/CRC},
author = {Gilchrist, Warren},
year = {2000},
keywords = {Distribution (Probability theory), Sampling (Statistics)},
file = {gilchrist_2000_statistical_modelling_with_quantile_functions.pdf:/home/dm0737pe/MEGA/ZoteroLibrary/gilchrist_2000_statistical_modelling_with_quantile_functions.pdf:application/pdf},
}