The asymptotic distributions of random sums

1989 ◽  
pp. 110-123
Author(s):  
V.Yu. Korolev
Keyword(s):  
Asymptotic Distributions ◽  
Random Sums

scholarly journals Small-sample asymptotic distributions of M-estimators of location

Biometrika ◽  
1982 ◽  
Vol 69 (1) ◽  
pp. 29-46 ◽  
Author(s):  
CHRISTOPHER A. FIELD ◽  
FRANK R. HAMPEL
Keyword(s):  
Small Sample ◽  
Asymptotic Distributions

scholarly journals Statistical Inference for the Beta Coefficient

Risks ◽  
2019 ◽  
Vol 7 (2) ◽  
pp. 56 ◽  
Author(s):  
Taras Bodnar ◽  
Arjun K. Gupta ◽  
Valdemar Vitlinskyi ◽  
Taras Zabolotskyy
Keyword(s):  
Confidence Interval ◽  
Empirical Study ◽  
Crucial Role ◽  
Risk Measure ◽  
Statistical Test ◽  
Asymptotic Distributions ◽  
Finite Sample ◽  
Benchmark Portfolio ◽  
Beta Coefficient ◽  
Theoretical Results

The beta coefficient plays a crucial role in finance as a risk measure of a portfolio in comparison to the benchmark portfolio. In the paper, we investigate statistical properties of the sample estimator for the beta coefficient. Assuming that both the holding portfolio and the benchmark portfolio consist of the same assets whose returns are multivariate normally distributed, we provide the finite sample and the asymptotic distributions of the sample estimator for the beta coefficient. These findings are used to derive a statistical test for the beta coefficient and to construct a confidence interval for the beta coefficient. Moreover, we show that the sample estimator is an unbiased estimator for the beta coefficient. The theoretical results are implemented in an empirical study.

scholarly journals On the Accuracy of the Generalized Gamma Approximation to Generalized Negative Binomial Random Sums

Mathematics ◽  
2021 ◽  
Vol 9 (13) ◽  
pp. 1571
Author(s):  
Irina Shevtsova ◽  
Mikhail Tselishchev
Keyword(s):  
Negative Binomial Distribution ◽  
Binomial Distribution ◽  
Law Of Large Numbers ◽  
Negative Binomial ◽  
Infinite Divisibility ◽  
Random Sums ◽  
Generalized Gamma ◽  
Second Moments ◽  
Large Numbers ◽  
Generalized Negative Binomial Distribution

We investigate the proximity in terms of zeta-structured metrics of generalized negative binomial random sums to generalized gamma distribution with the corresponding parameters, extending thus the zeta-structured estimates of the rate of convergence in the Rényi theorem. In particular, we derive upper bounds for the Kantorovich and the Kolmogorov metrics in the law of large numbers for negative binomial random sums of i.i.d. random variables with nonzero first moments and finite second moments. Our method is based on the representation of the generalized negative binomial distribution with the shape and exponent power parameters no greater than one as a mixed geometric law and the infinite divisibility of the negative binomial distribution.

Inference on P(Y

2020 ◽  
Vol 72 (2) ◽  
pp. 89-110
Author(s):  
Manoj Chacko ◽  
Shiny Mathew
Keyword(s):  
Maximum Likelihood ◽  
Pareto Distribution ◽  
Generalized Pareto Distribution ◽  
Maximum Likelihood Estimators ◽  
Record Values ◽  
Asymptotic Distributions ◽  
Bayes Estimators ◽  
Generalized Pareto ◽  
Pareto Distributions ◽  
Generalized Pareto Distributions

In this article, the estimation of [Formula: see text] is considered when [Formula: see text] and [Formula: see text] are two independent generalized Pareto distributions. The maximum likelihood estimators and Bayes estimators of [Formula: see text] are obtained based on record values. The Asymptotic distributions are also obtained together with the corresponding confidence interval of [Formula: see text]. AMS 2000 subject classification: 90B25

Nonnull asymptotic distributions of three classic criteria in generalised linear models

Biometrika ◽  
1994 ◽  
Vol 81 (4) ◽  
pp. 709-720 ◽  
Author(s):  
GAUSS M. CORDEIRO ◽  
DENISE A. BOTTER ◽  
SILVIA L. DE PAULA FERRARI
Keyword(s):  
Linear Models ◽  
Asymptotic Distributions ◽  
Generalised Linear Models
Sign in / Sign up

Export Citation Format

Share Document