Affiliations: [a] Indian Statistical Institute, Kolkata, West Bengal, India | [b] Department of Statistics, Burdwan University, Burdwan, West Bengal, India
Correspondence:
[*]
Corresponding author: Rabindra Nath Das, Department of Statistics, Burdwan University, Burdwan, West Bengal, India. E-mail:rabin.bwn@gmail.com
Abstract: The log-normal distribution arises in many
different domains such as finance, stock prices, risk assessments,
in motor and health insurance analysis, soil aggregate size
distributions (in agriculture), lifetime distributions (quality
engineering and survival analysis), telecommunications and traffic
engineering, and was introduced to model inherently positive,
continuous random phenomena. Positive observations from a
continuous random variable (with constant variance) are generally
analyzed either by log-normal or gamma models. However, in
practice, the variance is not constant always. For handling
non-constant variance in the log-normal process random variable
distribution, some concomitant variables are included as regressor
variables. In the present article, the response distribution is
assumed to be log-normal, and the errors under the process are
assumed to have a first-order autocorrelated structure. A
log-linear composite autocorrelated errors regression model has
been developed. The best linear unbiased estimators of all the
regression coefficients have been derived except for the intercept
which is often unimportant in practice. Autocorrelation
coefficient has been estimated by iterative method. A testing
procedure for any set of linear hypotheses regarding the unknown
regression coefficients has been developed. Confidence intervals
of an estimable function and confidence ellipsoids of a set of
estimable functions of regression coefficients have been
developed. An index of fit for the fitted regression model has
also been developed. An example (with
simulated data) illustrates the results derived in this report.
Keywords: Composite autocorrelated errors, confidence ellipsoid, confidence interval, index of fit, log-normal distribution
