The primary postpartum hemorrhage (PPH) as blood loss of

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.

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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:

.