FREQUENTLY USED SYMBOLS AND ABBREVIATIONS
- implies
- implies and is implied by
- converges to
- increasing, decreasing
- nonincreasing, nondecreasing
- Γ(x)
- gamma function
- limit superior, limit inferior, limit
, n- real line, n-dimensional Euclidean space
, n- Borel σ-field on , Borel σ-field on n
- IA
- indicator function of set A
(x)- = 1if x ≥ 0, and = 0 if x <0
- μ
- EX, expected value
- mn
- EXn, n ≥ 0 integral
- βα
- E|X|α,α> 0
- μk
- E(X — EX)k, k ≥ 0 integral
- σ2
- = μ2, variance
- f′, f″, f″′
- first, second, third derivative of f
- ~
- distributed as
- ≈
- asymptotically (or approximately) equal to
- convergence in law
- convergence in probability
- convergence almost surely
- convergence in rth mean
- RV
- random variable
- DF
- distribution function
- probability density function
- PMF
- probability mass function
- PGF
- probability generating function
- MGF
- moment generating function
- d.f.
- degrees of freedom
- BLUE
- best linear unbiased estimate
- MLE
- maximum likelihood estimate
- MVUE
- minimum variance unbiased estimate
- UMA
- uniformly most accurate
- UMVUE
- uniformly minimum variance unbiased estimate
- UMAU
- uniformly most accurate unbiased
- MP
- most powerful
- UMP
- uniformly most powerful
- GLM
- general linear model
- i.o.
- infinitely often
- iid
- independent, identically distributed
- SD
- standard deviation
- SE
- standard error
- MLR
- monotone likelihood ratio
- MSE
- mean square error
- WLLN
- weak law of large numbers
- SLLN
- strong law of large numbers
- CLT
- central limit theorem
- SPRT
- sequential probability ratio test
- b(1,p)
- Bernoulli with parameter p
- b(n,p)
- binomial with parameters n,p
- NB(r;p)
- negative binomial with parameters r,p
- Ρ(λ)
- Poisson with parameter λ
- U[a,b]
- uniform on [a, b]
- G(α,β)
- gamma with parameters α, β
- B(α,β)
- beta with parameters α, β
- χ2 (n)
- chi-square with d.f. n
(μ, θ)- Cauchy with parameters μ, θ
(μ,σ2)- normal with mean μ, variance σ2
- t(n)
- Student's t with n d.f.
- F(m, n)
- F-distribution with (m, n) d.f.
- zα
- 100(1 - α)th percentile of
(0,1) 
,α- 100(1 — α)th percentile of
2(n) - tn, α
- 100(1 — α)th percentile of t(n)
- Fm,n,α
- 100(1 — α)th percentile of F(m, n)
- AN
- asymptotically normal
- GLR
- generalized likelihood ratio
- MRE
- minimum risk equivariant
- ℓnx
- logarithm (to base e)of x
- exp(X)
- exponential
- LMP
- locally most powerful
(x)- law or distribution of RV X
- b(δ,.)
- bias in estimator δ
- iid
- independent, identically distributed
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