On Independence and Dependence Properties of a Set of Random Events

1993 ◽  
Vol 47 (2) ◽  
pp. 112 ◽  
Author(s):  
Y. H. Wang ◽  
Jordan Stoyanov ◽  
Qi-Man Shao
Keyword(s):  
Random Events ◽  
Dependence Properties

On Independence and Dependence Properties of a Set of Random Events

1993 ◽  
Vol 47 (2) ◽  
pp. 112-115
Author(s):  
Y. H. Wang ◽  
Jordan Stoyanov ◽  
Qi-Man Shao
Keyword(s):  
Random Events ◽  
Dependence Properties

scholarly journals EXACT LOWER BOUND ON AN ‘EXACTLY ONE’ PROBABILITY

2021 ◽  
pp. 1-7
Author(s):  
IOSIF PINELIS
Keyword(s):  
Lower Bound ◽  
Random Events

Abstract We obtain the exact lower bound on the probability of the occurrence of exactly one of n random events each of probability p.

scholarly journals Numerical estimates of risk factors contingent on credit ratings

2021 ◽  
Author(s):  
T. Gärtner ◽  
S. Kaniovski ◽  
Y. Kaniovski
Keyword(s):  
Risk Factors ◽  
Financial Risk ◽  
Credit Rating ◽  
Likelihood Function ◽  
Adverse Outcome ◽  
Credit Ratings ◽  
Industry Sector ◽  
Random Events ◽  
Historical Transition ◽  
Industry Sectors

AbstractAssuming a favorable or an adverse outcome for every combination of a credit class and an industry sector, a binary string, termed as a macroeconomic scenario, is considered. Given historical transition counts and a model for dependence among credit-rating migrations, a probability is assigned to each of the scenarios by maximizing a likelihood function. Applications of this distribution in financial risk analysis are suggested. Two classifications are considered: 7 non-default credit classes with 6 industry sectors and 2 non-default credit classes with 12 industry sectors. We propose a heuristic algorithm for solving the corresponding maximization problems of combinatorial complexity. Probabilities and correlations characterizing riskiness of random events involving several industry sectors and credit classes are reported.

On the distribution of the number of cyclically occurring random events

1972 ◽  
Vol 9 (3) ◽  
pp. 681-683
Author(s):  
Leon Podkaminer
Keyword(s):  
Random Variables ◽  
Independent Random Variables ◽  
Time Intervals ◽  
Time Period ◽  
Random Events ◽  
Mutually Independent

The probabilities of the occurrence of n events in a certain time period are calculated under the assumptions that the time intervals between the neighbouring events are mutually independent random variables, satisfying some analytic conditions.

Multivariate extremes, aggregation and dependence in elliptical distributions

2002 ◽  
Vol 34 (03) ◽  
pp. 587-608 ◽  
Author(s):  
Henrik Hult ◽  
Filip Lindskog
Keyword(s):  
Random Vector ◽  
Positive Constant ◽  
Tail Dependence ◽  
Constant Factor ◽  
Dispersion Matrix ◽  
Elliptical Distributions ◽  
Spectral Measures ◽  
Lower Tail ◽  
Explicit Formulae ◽  
Dependence Properties

In this paper, we clarify dependence properties of elliptical distributions by deriving general but explicit formulae for the coefficients of upper and lower tail dependence and spectral measures with respect to different norms. We show that an elliptically distributed random vector is regularly varying if and only if the bivariate marginal distributions have tail dependence. Furthermore, the tail dependence coefficients are fully determined by the tail index of the random vector (or equivalently of its components) and the linear correlation coefficient. Whereas Kendall's tau is invariant in the class of elliptical distributions with continuous marginals and a fixed dispersion matrix, we show that this is not true for Spearman's rho. We also show that sums of elliptically distributed random vectors with the same dispersion matrix (up to a positive constant factor) remain elliptical if they are dependent only through their radial parts.

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