Precise large deviations for the difference of two sums of random variables. Accepted.Lu D W, Song L X, Wang X H. Precise large deviation for the difference of two sums of random variables[J]. Communications in Statistics——Theory and Methods, 2016, 45(2): 291-306....
A chi-squared distribution cannot have zero degrees of freedom, so what would bethedistribution ofX−YX−Y? Supose that we have two random variablesX∼χ2kX∼χk2andY∼χ2kY∼χk2, with the same degrees of freedom. A chi-squared distribution cannot have zero degrees of freedom, s...
The Difference of Two Independent Exponential Random Variables iTunes This course is an introduction to probabilistic modeling, including random processes and the basic elements of statistical inference.
Before we can define a PDF or a CDF, we first need to understandrandom variables. Arandom variable,usually denoted asX, isa variablewhosevalues are numerical outcomesofsome random process. There aretwo typesofrandom variables:discreteandcontinuous. "Discrete"Random Variables A "discrete" random vari...
treatment is an example of a discrete random variable that can take on a finite number of values. The number of car accidents at an intersection is an example of a discrete random variable that can take on a countable infinite number of values (there is no fixed upper limit to the count...
This is the result of a few factors: The P/C industry is extremely competitive in Canada (insurers are always trying to find new ways to be more profitable and gain market share). P/C work deals with two random variables instead of just one on the SOA side. Pricing in P/C is based...
We let {A n} and {B n} be independent sequences of independent and identically distributed random variables, allowing general distributions, with A n and B n independent of X n1, where E[B n] = 0. This model is appealing because it can involve relatively few parameters, can be ...
We consider the theoretical aspects of the limiting behavior of these sequences. We give general conditions for the existence of limiting laws of the sequence { Y n} determined by Y n = U n + V n Y n1, where {( U n, V n)} is a given sequence of random variables. In the ...
(1) Systems of such equations appear naturally while studying weak generalized stabilities of random variables in [1]. Namely, the main problem of that paper has been reduced to determining Lebesgue (or Baire) measurable solutions f : (0, +∞) → (0, +∞) of the functional equation (f ...
Thesumof a pair of quantities is a single quantity -- the sum of a pair of random variables is a univariate random variable. The density function of the sum of independent variables goes from the sum of the smallest values of each variable to the sum of the largest values of each variab...