The and Mihran [111], Gomes et al. in 2008

The generalized gamma distribution (GGD)
was constructed by Stacy and Mihran 110 in an attempt to combine the power of
two distributions: the Gamma distribution and the Weibull distribution.  It is a newer distribution (1962) than the
normal distribution (1774). The generalized gamma distribution remains a renowned
distribution as this one stands exceptionally adaptable. This distribution is
too expedient because it comprises as special cases of quite a few
distributions: the exponential distribution, the log-normal distribution, the
Weibull distribution, the Levy distribution.

In cooperation the
exponential in addition to the more general Weibull distributions have
wide-spread usages in the exploration of engineering data. It is impartially
common habitation, however, to come across facts which are discordant through
these distributions and further accustomed probability models. Such data
kindles inference relating to the letdown systems besides added corporeal
marvels which may be involved. It also emboldens exploration to expand the
group of distributions which are useful to the enthusiastic statistician.

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The parameter
estimation of the generalized distribution was discussed by Stacy and Mihran 111, Gomes et al. in 2008 50 and the
Scheme of Parameter Estimation was discoursed by Gui Gao et al. 54. The
log–logistic distribution (LLD) and log normal distribution (LND) are commonly
used to examine the lifetime data. The LLD is derived from logistic
distribution (LD) by applying the logarithmic to LD in a similar way as LND is
obtained from normal distribution.

The LLD has
an alike shape related to LND but precisely more adaptable. It is renowned that
the log-logistics model is capable to model societal progressions with
monotonically declining, as well as non-monotonic, inverse type failure rates.
Several illustrations of flood frequency analysis used LLD was conferred by 2,
social diffusion model process using LLD was 32, 33 and economic reliability
using LLD was discussed by Kantam R R L 63.

Generalization
of LD and LLD was contested by Ojo 94. Recently the Balakrishnan skew
logistic distribution and its properties are discussed by Asgharzadeh 6. Skew
multivariate models related to hidden truncation and Censor order statistics
from log-logistic distribution with applications to inference was conferred by
Balakrishnan 11 and 10 respectively. The parameter estimation using maximum
entropy was conversed by Singh 109.

Oxytocin is a pituitary neuropeptide kind produced and discharge
by hypothalamus, at that time it is expected at the rear of pituitary to the far
side of hypothalamic–pituitary–adrenal axis at latter unconfined on the way to
blood. It can cause uterine contractions in labor and stimulate milk secretion,
100.  At present oxytocin consequence
on abirritaion has careworn far-reaching consideration. In addition its role of
delivery promotion, oxytocin can also be espoused in the pain factor in the
backbone and the periaqueductal gray of the brain, 132. Habenular nucleus
(Hb) is extensive in the dorsal diencephalon of vertebrates, and as an important
nucleus which participates in analgesia in central nervous system, it can be
divided into medial habenular nucleus (MHb) and lateral habenular nucleus (LHb)
{Fu et al.2010 45, Huang Min et al. 201160, Fu, 2006 44}, in which LHb,
as the junction of limbic system like amygdale, hippocampus, preoptic area,
etc. and midbrain, can regulate sleep and physiological process of
cardiovascular activity (Zhao and Wang, 131).

The natural roles of oxytocin in labor, milk letdown and social
affection were well-conserved 23, 49, 135.In modern ages, various
single-dose studies have been conducted on the effects of oxytocin on social
cognition in healthy humans 67 and 80. At present oxytocin consequence on
abirritaion has care worn far-reaching consideration; In addition, its role of
delivery promotion, oxytocin can also be espoused in the pain factor in the backbone
and the periaqueductal gray of the brain 132.

In our model 119, we study the
generalized gamma distribution in fuzzy environment and is used to analysis the
effect of dissimilar doses of oxytocin for the changes of hind paw with drawl latency of normal
mature mice. The mean and variance values of the fuzzy
generalized gamma distribution for different doses of oxytocin are calculated.