Geodesic
Nonparametric estimations of non-negative random variables distributions
Kybernetika, Tome 39 (2003) no. 3, pp. 341-346 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

The problem of estimation of distribution functions or fractiles of non- negative random variables often occurs in the tasks of risk evaluation. There are many parametric models, however sometimes we need to know also some information about the shape and the type of the distribution. Unfortunately, classical approaches based on kernel approximations with a symmetric kernel do not give any guarantee of non-negativity for the low number of observations. In this note a heuristic approach, based on the assumption that non-negative distributions can be also approximated by means of kernels which are defined only on the positive real numbers, is discussed.
The problem of estimation of distribution functions or fractiles of non- negative random variables often occurs in the tasks of risk evaluation. There are many parametric models, however sometimes we need to know also some information about the shape and the type of the distribution. Unfortunately, classical approaches based on kernel approximations with a symmetric kernel do not give any guarantee of non-negativity for the low number of observations. In this note a heuristic approach, based on the assumption that non-negative distributions can be also approximated by means of kernels which are defined only on the positive real numbers, is discussed.
Classification : 62G05, 62G07
Keywords: distribution function; kernelapproximation; non-negative random variable 
@article{KYB_2003_39_3_a9,
     author = {V\'avra, Franti\v{s}ek and Nov\'y, Pavel and Ma\v{s}kov\'a, Hana and Kotl{\'\i}kov\'a, Michala and Zmrhal, David},
     title = {Nonparametric estimations of non-negative random variables distributions},
     journal = {Kybernetika},
     pages = {341--346},
     year = {2003},
     volume = {39},
     number = {3},
     mrnumber = {1995738},
     zbl = {1245.62033},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2003_39_3_a9/}
}
TY  - JOUR
AU  - Vávra, František
AU  - Nový, Pavel
AU  - Mašková, Hana
AU  - Kotlíková, Michala
AU  - Zmrhal, David
TI  - Nonparametric estimations of non-negative random variables distributions
JO  - Kybernetika
PY  - 2003
SP  - 341
EP  - 346
VL  - 39
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/KYB_2003_39_3_a9/
LA  - en
ID  - KYB_2003_39_3_a9
ER  - 
%0 Journal Article
%A Vávra, František
%A Nový, Pavel
%A Mašková, Hana
%A Kotlíková, Michala
%A Zmrhal, David
%T Nonparametric estimations of non-negative random variables distributions
%J Kybernetika
%D 2003
%P 341-346
%V 39
%N 3
%U http://geodesic.mathdoc.fr/item/KYB_2003_39_3_a9/
%G en
%F KYB_2003_39_3_a9
Vávra, František; Nový, Pavel; Mašková, Hana; Kotlíková, Michala; Zmrhal, David. Nonparametric estimations of non-negative random variables distributions. Kybernetika, Tome 39 (2003) no. 3, pp. 341-346. http://geodesic.mathdoc.fr/item/KYB_2003_39_3_a9/

[1] German H.: Learning about risk: some lessons from insurance. European Finance Review 2 (1999), 113–124 | DOI

[2] Devroye L., Györfi L.: Nonparametric Density Estimation the $L_1$-view. Wiley, New York 1985 | MR

[3] Albrecher H.: Dependent Risks and Ruin Probabilities in Insurance. Interim Report, IIASA, IR 98 072

[4] Rao C. R.: Linear Statistical Inference and its Applications (Czech translation). Academia, Praha 1978

[5] Rényi A.: Theory of Probability (Czech translation). Academia, Praha 1972 | MR