Estimating the Fuzzy Survival Function of the Bure III Distribution updated with the Application

A thesis is  presented to the Council of College of Administration & Economics in University of Kerbalaa
As a part of MSc. Degree Requirements in Statistics

Presented by
Amal Mohammed Jawad Abdulkadhim Al Shaddood

Under supervision of
Asst. Prof.Dr. Moshtaq  Kareem Abdulraheem Asst. Prof.Dr.Bahaa  Abdulrazzaq Qasim

Abstract

Burr type III distribution with two parameters is deemed  one of the most important continuous probability  distributions  to analyze survival time for  several phenomenon  such as (premise include  birth, start  a  job,   till  ultimate event  include  pension  or death). In consequence, it is debated herein  the study of new modified    Burr III distribution; i.e., NMBIII, after adding  new   parameter  to Burr III Distribution  function  saving that we  did  not find  the such  new  distribution   but  in  one  research  work.

In this  study, it is argued   the characteristics  of  Mathematical statistic distribution in addition to the basic  concepts for   survival, risk, risk cumulative risk and  the basic concepts  of fuzzy sets, membership function and  definition of fuzzy  survival and then it is transferred to the empirical part of the study as it is accredited  Mont0carlo   Simulation  Mode  to generate data of different  pattern sizes  and  study several hypothetical patterns  for  shape   parameters(C,K)  and  scale  parameter(l) for new modified Burr III distribution(NBMIII), as  it is applied   three modes  to estimate   parameters (Maximum Likelihood Estimation (MLE) ,Ordinary Least Square (OLS) and CVS methods).  Then,  its  used parameters estimates were  collected   to find   the estimation of  survival  function and the fuzzy survival  functions  through comparison with IMSE,  Upon the  results of simulation , it is concluded that  the fuzzy  survival;  in case of  accrediting NMBIII; which is estimated by   MLE, is   the best method rather  than OLS and IMSE and CVM  as it is given  least integrated error of square  means   at   the pattern of maximum  size ( n=100).  In  regards to applied  part,  it is  used a local  real data  form   for a pattern consisted of 100 represent in survival times  alive for breast cancer  patients  and after comparing  the results of Goodness of fit  tests, it is stated that data   followed  the distribution,  and upon  differentiation among distribution. It is found  that  distribution in  case of fuzzy  data  is  better than the same   distribution in case of real data.

The study  concluded  several  findings; the most important of which,  the condition of died  in case of  that period of   illness  is   increased.   Thus, the researcher  recommended to provide   the required  and best therapy  by the  concerned  authorities  include  revealing  the community with the  importance  of early  test  to avoid  infection.

Estimating the Fuzzy Survival Function of the Bure III Distribution updated with the Application

A thesis is  presented to the Council of College of Administration & Economics in University of Kerbalaa
As a part of MSc. Degree Requirements in Statistics

Presented by
Amal Mohammed Jawad Abdulkadhim Al Shaddood

Under supervision of
Asst. Prof.Dr. Moshtaq  Kareem Abdulraheem Asst. Prof.Dr.Bahaa  Abdulrazzaq Qasim

Abstract

Burr type III distribution with two parameters is deemed  one of the most important continuous probability  distributions  to analyze survival time for  several phenomenon  such as (premise include  birth, start  a  job,   till  ultimate event  include  pension  or death). In consequence, it is debated herein  the study of new modified    Burr III distribution; i.e., NMBIII, after adding  new   parameter  to Burr III Distribution  function  saving that we  did  not find  the such  new  distribution   but  in  one  research  work.

In this  study, it is argued   the characteristics  of  Mathematical statistic distribution in addition to the basic  concepts for   survival, risk, risk cumulative risk and  the basic concepts  of fuzzy sets, membership function and  definition of fuzzy  survival and then it is transferred to the empirical part of the study as it is accredited  Mont0carlo   Simulation  Mode  to generate data of different  pattern sizes  and  study several hypothetical patterns  for  shape   parameters(C,K)  and  scale  parameter(l) for new modified Burr III distribution(NBMIII), as  it is applied   three modes  to estimate   parameters (Maximum Likelihood Estimation (MLE) ,Ordinary Least Square (OLS) and CVS methods).  Then,  its  used parameters estimates were  collected   to find   the estimation of  survival  function and the fuzzy survival  functions  through comparison with IMSE,  Upon the  results of simulation , it is concluded that  the fuzzy  survival;  in case of  accrediting NMBIII; which is estimated by   MLE, is   the best method rather  than OLS and IMSE and CVM  as it is given  least integrated error of square  means   at   the pattern of maximum  size ( n=100).  In  regards to applied  part,  it is  used a local  real data  form   for a pattern consisted of 100 represent in survival times  alive for breast cancer  patients  and after comparing  the results of Goodness of fit  tests, it is stated that data   followed  the distribution,  and upon  differentiation among distribution. It is found  that  distribution in  case of fuzzy  data  is  better than the same   distribution in case of real data.

The study  concluded  several  findings; the most important of which,  the condition of died  in case of  that period of   illness  is   increased.   Thus, the researcher  recommended to provide   the required  and best therapy  by the  concerned  authorities  include  revealing  the community with the  importance  of early  test  to avoid  infection.