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Invariant transformations to combine marginal probability functions to form multivariate distributions motivated by the need to enlarge the class of multivariate distributions beyond the multivariate normal distribution and its related functions such as the multi- variate Student's t-distribution and the Wishart distribution. An example is Frank's family of bivariate distributions. (The word 'copula' comes from Latin and means to connect or join.) Quintessentially copulas are measures of the dependent structure of the marginal distributions and they have been used to model correlated risks, joint default probabilities in credit portfolios and groups of individuals that are exposed to similar economic and physical environments. Also used in frailty models for surveying.
Multilevel models are the regression models for the multilevel or clustered data where units i are nested in the clusters j, for example a cross-sectional study where students are
Johnson-Neyman technique: The technique which can be used in the situations where analysis of the covariance is not valid because of the heterogeneity of slopes. With this method
Indirect least squares: An estimation technique used in the fitting of structural equation models. Commonly least squares are first used to estimate reduced form parameters. Usi
Regression to the mean is the procedure first noted by Sir Francis Galton that 'each peculiarity in man is shared by his kinsmen, but on average to the less degree.' Hence the ten
Negative binomial distribution is the probability distribution of number of failures, X, before the kth success in the sequence of Bernoulli trials where the probability of succes
A standard IQ test has a mean of 98 and a standard deviation of 16. We want to be 99% certain that we are within 8 IQ points of the true mean. Determine the sample size
Hurdle Model: The model for count data which postulates two processes, one generating the zeros in the data and one generating positive values. The binomial model decides the bina
Response surface methodology (RSM): The collection of the statistical and mathematical methods useful for improving, developing, and optimizing processes with significant applicat
Multiple correlation coefficient is the correlation among the observed values of dependent variable in the multiple regression, and the values predicted by estimated regression
Prepare a 1,400- to 1,750-word paper in which you formulate a hypothesis based on your selected research issue, problem, or opportunity. Address the following: •Describe your sele
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