The importance of the

techniques used in a statistical investigation rest on extremely on the

presumed probability model or distribution. The purpose of statistical

interpretation is to draw decisions about a population on the source of data

acquired from a sample of that population. Hypothesis testing is the procedure

used to assess the strength of evidence from the sample and provides a basis

for making choices related to the population, i.e., it provides a technique for

understanding how consistently one can generalize experiential ?ndings in a

sample under study to the higher population from which the sample was taken. Buckley

15 produced a fuzzy test statistic by apply a fuzzy estimator in hypothesis

testing. Tests on variance unknown and tests on binomial and normal population

one should refer Buckley 14. Gholamreza Hesamian, Mehdi Sham 48 proposed a

method using parametric testing statistical hypotheses for fuzzy random

variables. Fuzzy hypothesis testing

using likelihood ratio statistic was developed by ShimaYose?etc 107. A new

approach for testing fuzzy hypothesis based on fuzzy data was discussed by

Mohsen Arefi, S. Mahmoud Taheri 86. A classical one-sided hypothesis testing

problem about the population mean for interval data was conversed by Przemys?aw

etc. 99. OlgierdHryniewicz etc. 95 proposed a methodology for Bayes

statistical decision analysis is to compare fuzzy risks related to considered

decisions for the case of reliability using Weibull distribution. The

haemodynamic effects of an oxytocin bolus involve of complete vasodilatation,

with hypotension, tachycardia, and intensification in cardiac output and

respiratory blood vessel pressure, causing in brief hypotension and tachycardia

in a dose-dependent manner. World Health Organization (WHO) defines primary

postpartum hemorrhage (PPH) as blood loss of greater than or equal to 1000 ml

following cesarean section (CS) 55. It accounts for one-quarter of the major

direct causes of maternal deaths globally 117, while it rises up to nearly

one-third of mortalities in Africa and Asia 65. The risk of postpartum

complications in women who received a CS was higher than that in women who

underwent a vaginal delivery (VD) and vaginal birth after cesarean section

(VBAC) 41, 79. The incidence of PPH has been reported to be 3.9% in women

delivered vaginally and reaches 7.9% after CS 91.

This chapter organized

as follows, in section 4.2. and 4.3 we are using the fuzzy mathematical model

based on the generalized gamma distribution (GGD), log-logistic distribution

(LLD), generalized Rayleigh distribution (GRD) and Rayleigh distribution (RD) those

are discussed in chapter 2 and 3. The mean and variance value for respiratory

changes, cardiac output, heart rate and stroke volume are calculated for

finding the effect of oxytocin in PPH. In section 4.4., using testing of

hypothesis we compare the mean values and variance of the various models. Abrief

conclusion is delivered in section 4.5.

4.1.

Application

I

Consider a trail

conducted by Ahmed 4, for prevention of postpartum hemorrhage (PPH) after

cesarean section by administrating the study drug oxytocin. The study was

conducted on 150 patients after fetal extraction. The respiratory changes were

given in the Fig. 4.1.Based on that study the

parameters of GGD are 1.0272, 71.316, 0.3455, the LLD parameters are 10.986,

21.107, the parameters of GRD are 16.932, 4.0012 and the parameter of RD is

17.5530. The corresponding fuzzy

triangular numbers of the GGD parameters

are

0.9601, 1.0272, 1.1118,

70.0341, 71.3160, 72.6905,

0.3428, 0.3455, 0.3500.

The corresponding

–cuts are

0.9601+0.0671a,

1.0272, 1.1118-0.0846a,

70.0341+1.2819a,

71.3160, 72.6905-1.3745a, and

. 0.3428+0.0027a,

0.3455, 0.3500-0.0045a.

The fuzzy triangular numbers of the LLD parameters are

9.9623, 10.8600, 12.0283,

19.8328, 21.1070, 22.4751.

The corresponding

–cuts are

9.9623+1.0237a,

10.8600, 12.0283-1.0423a,

19.8328+1.2742a,

21.1070, 22.4751-1.3681a.

The fuzzy triangular numbers of the GRD parameters are

15.9023, 16.9320, 17.9806,

3.0589, 4.0012, 4.8743.

The corresponding a–cuts

are

15.9023+1.0297a,

16.9320, 17.9806-1.0486a,

3.0589+0.9423a,

4.0012, 4.8743-0.8731a.

The fuzzy triangular number for RD

parameter is

16.7484, 17.5530, 18.2982.

The corresponding

–cut is

16.7484+0.8046a,

17.5530, 18.2982-0.7452a.

The Fuzzy mean values and variance for

FLLD, FGGD, FGRD and FRD are calculated based on equations (2.7), (2.9),

(2.17), (2.19), (3.12), (3.14), (3.26), (3.28) and it is presented in the Tables

4.1. and 4.2. for lower and upper alpha cuts respectively.Oxytocin is given normally

at caesarean unit to decrease the occurrence and sternness of post-partum hemorrhage.

The haemodynamic consequence of oxytocin get little consideration in

pharmacology scripts, however may be clinically substantial in vulnerable

patients. Consider the randomized, double blind experiment presented by A.J.

Pinder et al. 96 for haemodynamic effects

triggered by rapid bolus of 5 or 10 units of oxytocin in thirty-four patients

at caesarean unit beneath backbone anaesthesia. After administration of

oxytocin the heart rate (HR), stroke volume (SV) and cardiac output (CO) was

measured and is shown in the Fig. 4.6., Fig. 4.7.and Fig. 4.8. respectively.4.1.

Testing

of HypothesisTesting

statistical hypotheses is one of the most important parts of statistical

inference. Hypothesis

testing is the process used to extent the strength of validation from the trial

and offers a plan for making decisions related to the population, i.e., it

conveys a technique for accepting how consistently one can deduce experimental

?ndings in a sample under study to the greater population from which the sample

was drawn. In the statistical decision theory, we deal with

various amounts of data which may be vague and imprecise. Our observation may

be imprecise, described in linguistic terms. In such a case we deal with

imprecise (fuzzy) statistical data. We

analyze 120, 124 the FLLD, FGGD, FGRD, FRD by testing of hypothesis.

We first define a hypothesis – a certain declaration

of the population parameters, such a hypothesis denoted by H0. Here

we define the H0 as H0:

there is a significant difference in

than

and H1:

.