Glossary

= A-C =

A

 * Absorbing barrier	:


 * Asymptotic distribution:

B

 * bayes theorem: Thomas Bayes


 * bernoulli trial:


 * binomial distribution:

C

 * chebyshevs inequality:


 * conditional distribution:


 * conditional probability:


 * Consistency: An estimator is said to be consistent if the probability of it differing from the true value \theta by more than any positive value e tends towards 0 as the sample size increases

Confidence Interval

= D-F =

D

 * demography:	study of human populations

E

 * equilibrium distribution:

Event space


 * event:

= G-I =

G

 * Gamma distribution:


 * Gamma function:

I

 * invariant distributions: also stationary distributions

= J-L =

J

 * Joint probability distribution:

L

 * Limiting distribution:

= M-O =

M

 * Marginal distribution: marginal distribution of a subset of a collection of random variables is the probability distribution of the variables contained in the subset. The term marginal variable is used to refer to those variables in the subset of variables being retained.

every random walk is a Markov chain	,not every markov chain is a random walk
 * Markov Chain	:in general a stochastic process in discrete time is said to have the Markov property


 * Markov Property:For some random walk, the distribution of Xn is determined by Xn-1 and Zi and Xn-2 and Xn-3 are irreleveant


 * Moments of a distribution:

N

 * New better than used: NBU The older the component gets, the more likely it is to fail


 * New worse than used: (NWU)

= P-R =

P

 * pareto distribution:


 * point process	:


 * Poisson distribution:


 * population ecology:the study of how more general populations interact with their environment and with other populations

R

 * Random Walk:A random process {Xn; n = 0,1,2,....} is a random walk if for n>=1 Xn = Xn-1 + Zn A feature of a random walk is that the increments are independent identically distributed random variables


 * Recurrent Random Walk	:	 The return to the origin is only certain when the random walk is symmetric, that is when p = q= ½ and in this case the random walk is said to be recurrent


 * Renewal processes:are an idealized stochastic model for events that occur randomly in time (generally called renewals or arrivals). The basic mathematical assumption is that the times between successive arrivals are independent and identically distributed.

= S-U =

S

 * Sampling distribution:


 * Simple Random Walk :If the only possible values of Zi are -1, 0 and 1 then the process is a simple random walk


 * Standard Error: The standard deviation of the sampling distribution of the statistic is referred to as the standard error of that quantity.


 * Stationary Transition probabilities	:


 * stationary population	:


 * Statistic: (singular) is a single measure of some aspect of a sample, by applying a function to the values of the data, e.g. calculation of the mean. In the formal sense the function of the statistic in independent of the data itself, hence the function is known before the data is observed. The term statistic is used to refer to both the function, and for the realized value of the function on some observed sample of data.


 * Stochastic process	:@todo even if the initial states are known there is indetermenancy of the subsequent stats

T

 * Type I error: reject uppercase H_0 when it is true.


 * Type II error: do not reject H_0 when it is false.


 * Transient random walk: When p > q or q > p a particle is not certain to return to the origin; there is a positive probability that the particle will never return and in this case the random walk is said to be transient.


 * Transition probabilities	:the transition probabilities do not change with time
 * Transient Random Walk:


 * transition distribution: the probability model which links the future value of the Markov chain with the present one. $$P(X_t+1 | X_t=x_t)$$


 * transition kernel:


 * transition matrix:

U
= V-X =

W

 * Wasserstein: metric is a distance function defined between probability distributions on a given metric space M.


 * wald statistic:

= Y-Z =