When [alpha] =2 and [alpha] =1, the PDF in (3) has a closed-form expression, and the S[alpha]S distribution reduces to a Gaussian distribution and

Cauchy distribution, respectively.

The distributions of the error term e and the predictors are contaminated by two types of distributions, t distribution with 5 degrees of freedom ([t.sub.(5)]) and

Cauchy distribution with mean equal to 0 and variance equal to 1 (Cauchy (0, 1)).

To address these issues, this paper proposes a novel version of TLBO that is augmented with error correction and

Cauchy distribution (ECTLBO) in which the

Cauchy distribution is utilized to expand the searching space and error correction to avoid detours to achieve more accurate solutions.

The standard

Cauchy distribution (Student's t-distribution with one degree of freedom) has neither a moment-generating function nor finite moments of order greater than or equal to one [Johnson et al., 1994].

Very briefly, the

Cauchy distribution has unknown mean and variance, but defined median and mode.

Otherwise the notations [[[lambda].sub.E], RE} are often used in papers for second case due to relation between

Cauchy distribution for f(x) and exponential parametrization for Bose-Einstein CF [C.sub.2](q) discussed above.

The newly proposed algorithm uses the concept of

Cauchy distribution to follow large steps in global pollination, enhanced local search and dynamic switch probability to control the rate of local and global pollination.

where [u.sub.Cauchy] is the random number between 0 and 1 and the generated value [u.sub.Cauchy] is subjected to the

Cauchy distribution.

Distribution Form of distribution Beta distribution f(x; [alpha], [beta]) = [1/B([alpha], [beta])][x.sup.[alpha]-1][(1 - x) .sup.[beta]-1]

Cauchy distribution f(x; [x.sub.0], [gamma]) = [1/n] {[gamma]/[[(x - [x.sub.0]).sup.2] + [gamma]]} Chi-square distribution [mathematical expression not reproducible] Continuous uniform f(x) = [1/[b - a]] a [less than or distribution equal to] x [less than or equal to] b Gamma distribution f(x; k, [theta]) = [1/[[theta].sup.k]] [1/[GAMMA](k)][x.sup.k-1][e.sup.-x/ [theta]] Inverse-chi-squared f(x; k) = [[2.sup.-k/2]/[GAMMA] distribution (k/2)][x.sup.-k/2-1][e.sup.-1/2x] Inverse Gamma f(x; [alpha], [beta]) = [[[beta].sup.

For example

Cauchy distribution sample TLM were unbiased to the corresponding population quantities and more robust to outliers as reported by (Elamir and Seheult, 2003).

Note [F.sub.m] is initialized with value of 0.5 while

Cauchy distribution prevent premature convergence due to its wider tail property.

Thus, for the standard

Cauchy distribution [[sigma].sup.2] [right arrow] [infinity] but MAD = 1.