Obținerea de selecții simulate cu Excel în cazul variabilelor probabiliste discrete și continue - metoda Monte Carlo

I. Procedura pentru aplicarea metodei Monte Carlo în cazul variabilelor probabiliste discrete

Distribuţii discrete de probabilitate

empirică discretă

uniformă discretă

binomială

Poisson ….

II. Procedura pentru aplicarea metodei Monte Carlo în cazul variabilelor probabiliste continue

Distribuţii continue de probabilitate

empirică continuă

uniformă continuă

triunghiulară

normală

exponentială …

O v.a. este o cantitate masurata in legatura cu un experiment aleator;

O „variabilă aleatoare” sau o „distribuţie” nu este altceva decât un alt mod de a descrie rezultatul unui experiment aleator.

V.a – sunt importante deoarece asigura obiectivitate in reproducerea /replicarea unor rezultate ale unor evenimente (prin verificabilitate, reproductibilitate). Analistul/decidentul/cercetatorul alege procentajul din masa de evenimente replicate care ar trebui in principiu sa conduca la rezultate similare (sa fie acceptate in baza formularii ipotezei verificate ca fiind CORECTA, si sa respinga ipoteza FALSA), permitand variabilitatea rezultatelor.

Nivel de incredere: 1 − α = 0.90, 0.95, 0.99

Nivel de semnificatie: α = 0.10, 0.05, 0.01(erori acceptate)

► Numerice

Discrete vs. continue

► Categoriale

Nominale/ordinale

Ex1: succes/esec

Ex2: categorii: note/scoruri:1, 2, 3 … , ani 2010, 2011, etc. sau clase: I, II, III etc. sau atribute calitative

f(x) functie de masa/densitate de probabilitate

F(x) functie de repartitie

Indicatori statistici:

medie,

dispersie, abatere standard

etc.

a probability mass function (pmf) is a function that gives the probability that a discrete random variable is exactly equal to some value. A pmf differs from a probability density function (pdf) in that the values of a pdf, defined only for continuous random variables, are not probabilities as such. Instead, the integral of a pdf over a range of possible values (a, b] gives the probability of the random variable falling within that range.

Suppose that X: S → R is a discrete random variable defined on a sample space S. Then the probability mass function fX: R → [0, 1] for X is defined as

Note that fX is defined for all real numbers, including those not in the image of X; indeed, fX(x) = 0 for all x X(S).

Since the image of X is countable, the probability mass function fX(x) is zero for all but a countable number of values of x.

The discontinuity of probability mass functions reflects the fact that the cumulative distribution function of a discrete random variable is also discontinuous. Where it is differentiable, the derivative is zero, just as the probability mass function is zero at all such points.

a probability density function (abbreviated as pdf, or just density) of an absolutely continuous random variable is a function that describes the relative chance for this random variable to occur at a given point in the observation space. The probability for a random variable to fall within a given set is given by the integral of its density over the set.

The terms  “probability distribution function” and  “probability function” have also been used to denote the probability density function.