Prilog___

Prilog___Statistike formule za menadment i ekonomiju

Statistics for Management and Economics Formulas

Numerike deskriprivne tehnike (Numerical Descriptive techniques)Sredina populacije (Population mean) =

Sredina uzorka (Sample mean)

Rang (Range)Najvia opservacija-Najnia opservacija (Largest observation - Smallest observation)Varijansa disperzija populacije (Population variance) =

Varijansa disperzija uzorka (Sample variance) =

Standardna devijacija populacije (Population standard deviation) =

Standardna devijacija uzorka (Sample standard deviation)

s =

Kovarijansa populacije (Population covariance)

Kovarijansa uzorka (Sample covariance)

Koeficijent korelacije populacije (Population coefficient of correlation)

Koeficijent korelacije uzorka (Sample coefficient of correlation)

Koeficijent determinisanosti (Coefficient of determination)

R2 = r2Koeficijent nagiba (Slope coefficient)

y odseak (y-intercept)

Verovatnoa (Probability)Uslovna verovatnoa (Conditional probability) P(A|B) = P(A and B)/P(B)

Pravilo komplimenta (Complement rule) P() = 1 P(A)

Pravilo mnoenja (Multiplication rule) P(A and B) = P(A|B)P(B)

Pravilo sabiranja (Addition rule) P(A or B) = P(A) + P(B) - P(A and B)

Bayes-ova formula (Bayes Law Formula)

Sluajna promenljiva i distribucija verovatnoe diskretne promenljive (Random Variables and Discrete Probability Distributions)

Ocenjena vrednost sredina (Expected value -mean)

E(X) =

Varijansa disperzija (Variance)

V(x) =

Standardna devijacija (Standard deviation)

Kovarijansa (Covariance)

COV(X, Y) = xy =

Koeficijent korelacije (Coefficient of Correlation)

Pravila ocene vrednosti (Laws of expected value)

1. E(c) = c

2. E(X + c) = E(X) + c

3. E(cX) = cE(X)

Prvaila varijanse disperzije (Laws of variance)

1.V(c) = 0

2. V(X + c) = V(X)

3. V(cX) = V(X)

Pravila ocene vrednosti i varijanse zbira dve promenljive (Laws of expected value and variance of the sum of two variables)

1. E(X + Y) = E(X) + E(Y)

2. V(X + Y) = V(X) + V(Y) + 2COV(X, Y)

Pravila ocene vrednosti i varijansa zbira vie od dve promenljive (Laws of expected value and variance for the sum of more than two variables)

1.

2. if the variables are independent

Sredina i varijansa za portfolio od dva skupa (Mean and variance of a portfolio of two stocks) E(Rp) = w1E(R1) + w2E(R2)

V(Rp) = V(R1) + V(R2) + 2

EMBED Equation.3 COV(R1, R2)

=

EMBED Equation.3 +

EMBED Equation.3 + 2

EMBED Equation.3

EMBED Equation.3

EMBED Equation.3

EMBED Equation.3 Sredina i varijansa za portfolio od k skupova (Mean and variance of a portfolio of k stocks)

E(Rp) =

V(Rp) =

Binomna verovatnoa (Binomial probability)

P(X = x) =

EMBED Equation.3

Poisson-ova (Poisson probability) P(X = x) =

Distribucija verovatnoe kontinuirane promenljive (Continuous Probability Distributions)

Standardna normalna sluajna promenljiva (Standard normal random variable)

Eksponencijalna distribucija (Exponential distribution)

F distribucija (F distribution)

=

Distribucija uzorka (Sampling Distributions)

Ocena vrednosti sredine uzorka (Expected value of the sample mean)

EMBED Equation.3 Varijansa sredine uzorka (Variance of the sample mean)

EMBED Equation.3 Standardna greka sredine uzorka (Standard error of the sample mean)

Standardizaccija sredine uzorka (Standardizing the sample mean)

Ocena vrednosti proorcije uzorka (Expected value of the sample proportion)

EMBED Equation.3 Varijansa disperzija proporcije uzorka (Variance of the sample proportion)

Standardna greka proporcije uzorka (Standard error of the sample proportion)

Standardizacija proporcije uzorka (Standardizing the sample proportion)

Ocena vrednosti razlike izmeu dve sredine (Expected value of the difference between two means)

EMBED Equation.3 Varijansa disperzija razlike izmeu dve sredine (Variance of the difference between two means)

Standardna greka razlike izmeu dve sredine (Standard error of the difference between two means)

Standardizacija rezlike izmeu dve sredine uzorka (Standardizing the difference between two sample means)

Uvod u ocenu (Introduction to Estimation)Interval poverenja estimatora (Confidence interval estimator of )

Veliina uzorka za ocenu (Sample size to estimate )

Uvod u testiranje hipoteza (Introduction to Hypothesis Testing)Test statistika za (Test statistic for)

Zakljuivanje o populaciji (Inference about One Population)Test statistika za (Test statistic for )

Interval poverenja estimatora (Confidence interval estimator of )

Test statistika za (Test statistic for )

Interval poverenja estimators (Confidence interval Estimator of ) LCL =

UCL =

Test statistika za p (Test statistic for p)

Interval poverenja estimatora p (Confidence interval estimator of p)

Veliina uzorka za ocenu p (Sample size to estimate p)

Interval poverenja estimatora ukupne ograniene populacije (Confidence interval estimator of the total of a large finite population)

Interval poverenja estimatora ukupnog broja uspenih u ogranienoj populaciji (Confidence interval estimator of the total number of successes in a large finite population)

Interval poverenja estimatora kada je populacija mala (Confidence interval estimator of when the population is small)

Interval poverenja estimatora ukupne male populacije (Confidence interval estimator of the total in a small population)

Interval poverenja estimatora p kada je populacija mala (Confidence interval estimator of p when the population is small)

Interval poverenja estimatora ukupnog broja uspenih u maloj populaciji (Confidence interval estimator of the total number of successes in a small population)

Zakljuivanje o dve populacije (Inference About Two Populations)Jednake varijanse t-test (Equal-variances t-test of )

Jednake varijanse interval estimator (Equal-variances interval estimator of )

Nejednake varijanse t-test (Unequal-variances t-test of )

Nejdnake varijanse interval estimator (Unequal-variances interval estimator of )

t-test (t-Test of )

t-estimator (t-Estimator of )

F-test (F-test of )

F =

and

F-estimator (F-Estimator of ) LCL =

UCL =

z-test estimator (z-Test and estimator of ) Case 1:

Case 2:

z estimator (z-estimator of )

Analiza varijanse (Analysis of Variance)Jedan nain analize varijanse (One-way analysis of variance) SST =

SSE =

MST =

MSE =

F =

Drugi nain analize varijanse (Two-way analysis of variance -randomized block design of experiment)

SS(Total) =

SST =

SSB =

SSE =

MST =

MSB =

MSE =

F =

F=

Dvo-faktorski eksperiment (Two-factor experiment)

SS(Total) =

SS(A) =

SS(B) =

SS(AB) =

SSE =

F =

F =

F =

Najmanja znaajna razlika Metod komparacije (Least Significant Difference Comparison Method) LSD =

Tukeys-ov multiple komparacioni metod (Tukeys multiple comparison method)

Hi-kvadrat test (Chi-Squared Tests)Test statistika za sve procedure (Test statistic for all procedures)

Linerana regresija uzorka (Simple Linear Regression)Nagib uzorka (Sample slope)

y-odseak uzorka (Sample y-intercept)

Zbir kvdrata greke (Sum of squares for error)

SSE =

Standardna greka estimacije (Standard error of estimate)

Test statistika za nagib (Test statistic for the slope)

Standardna greka od (Standard error of )

Koeficijen determinisanosti (Coefficient of determination)

Interval predvianja (Prediction interval)

Interval poverenja estimatora ocenjene vrednosti y (Confidence interval estimator of the expected value of y)

Koeficijent korelacije uzorka (Sample coefficient of correlation)

Test statistika za testiranje = 0 ( Test statistic for testing = 0)

Multiple regresija (Multiple Regression)Standardna greek estimacije (Standard Error of Estimate)

Test statistika za (Test statistic for )

Koeficijent determinisanosti (Coefficient of Determination)

Prilagoeni koeficijent determinisanosti (Adjusted Coefficient of Determination)

Adjusted

Kvadrat sredine greke (Mean Square for Error)

MSE = SSE/k

Kvdrat sredine za regresiju (Mean Square for Regression)

MSR = SSR/(n-k-1)

F-statistika (F-statistic)

F = MSR/MSE

Durbin- Watson-ova statistika (Durbin-Watson statistic)

Neparametarske statistike tehnike (Nonparametric Statistical techniques)Wilcoxon rang - zbir test statistika (Wilcoxon rank sum test statistic)

E(T) =

Znak test statistika (Sign test statistic)x = number of positive differences

Wilcoxon-ov rang znaajnosti zbira test statistike (Wilcoxon signed rank sum test statistic)

E(T) =

Kruskal Wallis ov test (Kruskal-Wallis Test)

Friedman-ov test (Friedman Test)

Spearman ov koeficijent korelacije (Spearman rank correlation coefficient)

Spearman-ova test statistika za n > 30 (Spearman Test statistic for n > 30)

Analiza vremenskih serija i predvianje (Time Series Analysis and Forecasting)

Eksponencijalno izravnanje (Exponential smoothing)

Statistiki proces kontrole (Statistical Process Control)

Srednja linija i kontrolni nivoi za dijagram korienjem S (Centerline and control limits for chart using S) Srednja linija (Centerline) =

Donji kontrolna granica (Lower control limit) =

Gornji kontrolna granica (Upper control limit) =

Srednja linija i kontrolna granica za p dijagram (Centerline and control limits for the p chart)

Srednja linija (Centerline) =

Donja kontrolna granica (Lower control limit) =

Gornja kontrolna granica (Upper control limit) =

Analiza odluivanja (Decision Analysis)Ocenjena vrednost savrene informacje (Expected Value of perfect Information) EVPI = EPPI - EMV*

Ocenjena vrednost informacije uzorka (Expected Value of Sample Information) EVSI = EMV' - EMV*

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