The importance of thetechniques used in a statistical investigation rest on extremely on thepresumed probability model or distribution.
The purpose of statisticalinterpretation is to draw decisions about a population on the source of dataacquired from a sample of that population. Hypothesis testing is the procedureused to assess the strength of evidence from the sample and provides a basisfor making choices related to the population, i.e.
, it provides a technique forunderstanding how consistently one can generalize experiential ?ndings in asample under study to the higher population from which the sample was taken. Buckley15 produced a fuzzy test statistic by apply a fuzzy estimator in hypothesistesting. Tests on variance unknown and tests on binomial and normal populationone should refer Buckley 14. Gholamreza Hesamian, Mehdi Sham 48 proposed amethod using parametric testing statistical hypotheses for fuzzy randomvariables. Fuzzy hypothesis testingusing likelihood ratio statistic was developed by ShimaYose?etc 107.
A newapproach for testing fuzzy hypothesis based on fuzzy data was discussed byMohsen Arefi, S. Mahmoud Taheri 86. A classical one-sided hypothesis testingproblem about the population mean for interval data was conversed by Przemys?awetc.
99. OlgierdHryniewicz etc. 95 proposed a methodology for Bayesstatistical decision analysis is to compare fuzzy risks related to considereddecisions for the case of reliability using Weibull distribution. Thehaemodynamic effects of an oxytocin bolus involve of complete vasodilatation,with hypotension, tachycardia, and intensification in cardiac output andrespiratory blood vessel pressure, causing in brief hypotension and tachycardiain a dose-dependent manner. World Health Organization (WHO) defines primarypostpartum hemorrhage (PPH) as blood loss of greater than or equal to 1000 mlfollowing cesarean section (CS) 55. It accounts for one-quarter of the majordirect causes of maternal deaths globally 117, while it rises up to nearlyone-third of mortalities in Africa and Asia 65.
The risk of postpartumcomplications in women who received a CS was higher than that in women whounderwent 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 womendelivered vaginally and reaches 7.9% after CS 91.This chapter organizedas follows, in section 4.
2. and 4.3 we are using the fuzzy mathematical modelbased on the generalized gamma distribution (GGD), log-logistic distribution(LLD), generalized Rayleigh distribution (GRD) and Rayleigh distribution (RD) thoseare discussed in chapter 2 and 3. The mean and variance value for respiratorychanges, cardiac output, heart rate and stroke volume are calculated forfinding the effect of oxytocin in PPH. In section 4.
4., using testing ofhypothesis we compare the mean values and variance of the various models. Abriefconclusion is delivered in section 4.5.
4.1. ApplicationIConsider a trailconducted by Ahmed 4, for prevention of postpartum hemorrhage (PPH) aftercesarean section by administrating the study drug oxytocin. The study wasconducted on 150 patients after fetal extraction. The respiratory changes weregiven in the Fig. 4.
1.Based on that study theparameters 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 is17.5530. The corresponding fuzzytriangular numbers of the GGD parametersare 0.9601, 1.0272, 1.
1118, 70.0341, 71.3160, 72.6905, 0.3428, 0.3455, 0.3500.The corresponding –cuts are 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–cutsare 15.9023+1.0297a,16.9320, 17.9806-1.0486a, 3.
8731a. The fuzzy triangular number for RDparameter 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 forFLLD, 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 Tables4.
1. and 4.2. for lower and upper alpha cuts respectively.
Oxytocin is given normallyat caesarean unit to decrease the occurrence and sternness of post-partum hemorrhage.The haemodynamic consequence of oxytocin get little consideration inpharmacology scripts, however may be clinically substantial in vulnerablepatients. Consider the randomized, double blind experiment presented by A.J.Pinder et al. 96 for haemodynamic effectstriggered by rapid bolus of 5 or 10 units of oxytocin in thirty-four patientsat caesarean unit beneath backbone anaesthesia. After administration ofoxytocin the heart rate (HR), stroke volume (SV) and cardiac output (CO) wasmeasured and is shown in the Fig.
4.6., Fig. 4.7.and Fig.
1. Testingof HypothesisTestingstatistical hypotheses is one of the most important parts of statisticalinference. Hypothesistesting is the process used to extent the strength of validation from the trialand offers a plan for making decisions related to the population, i.e., itconveys a technique for accepting how consistently one can deduce experimental?ndings in a sample under study to the greater population from which the samplewas drawn. In the statistical decision theory, we deal withvarious amounts of data which may be vague and imprecise. Our observation maybe imprecise, described in linguistic terms.
In such a case we deal withimprecise (fuzzy) statistical data. Weanalyze 120, 124 the FLLD, FGGD, FGRD, FRD by testing of hypothesis. We first define a hypothesis – a certain declarationof the population parameters, such a hypothesis denoted by H0. Herewe define the H0 as H0: there is a significant difference in than and H1: .