Title of Thesis

Stochastic Models For Population of Pakistan.

Author(s)

Muhammad Zakria

Abstract
Population of Pakistan is projected by scientists, bureaus and countries using different methodologies. In this study, population projections, its age-sex distribution vision 2030 and inequality of the recorded and projected age-sex distribution is projected by different methods. Moreover, the reproductive cohort measure and fertility trends of the population during the last 20 years are measured. The said goals are achieved by using the population censuses data.
First of all, the quality of all censuses data is checked and found to be very poor especially of 1972 census.Different popular smoothing techniques are used to smooth the census data and strong smoothed data is used for further analysis. A time series model i.e. ARIMA (1, 2, 0) W was found to be a parsimonious model and population is projected for the next 20 years.It would be approximately 230.68 million in 2027 along with 95% confidence limits 193.33 million and 275.25 million.The age sex distribution as well as the total population is also projected by using the Modified Markov chain method for 40 years ahead since 1981.The Projections by the Time series models and the Modified Markov chain method are more close to the projections of four internationally known
bureaus i.e. (WPP 2008; People Facts and Figures & Total Population by Country 2009) and greater than (NIPS 2006; IDB 2008). Gini coefficients of the projected age sex distribution indicated the medium level of concentration during the next 20 years.
Approximately 43.74%, 47.27% and 45.46% decrease in TFR has been seen in rural areas, urban areas and in Pakistan respectively during 1984-2005.Different polynomial models are studied and third degree polynomial model is recommended to fit on the age specific fertility rates of Pakistan and its rural urban regions.

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2.1 Introduction
2.2 Accuracy of Population Census Data
2.3 Population Projection
2.4 Transition Probabilities and Population inequality
2.5 Fertility Analysis Modeling

3.1 Introduction
3.2 Objectives
3.3 Methodology
3.4 Results and Discussion
3.5 Conclusion and Recommendations

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4.1 Introduction
4.2 Objectives
4.3 About the Data
4.4 Methodology
4.5 Results and Discussion
4.6 Conclusion and Recommendations

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5.1 Introduction
5.2 Objectives
5.3 About the Data
5.4 Methodology
5.5 Results and Discussion
5.6 Conclusion and Recommendations

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6.1 Introduction
6.2 Objectives
6.3 About the Data
6.4 Modified Markov Chain Models
6.5 Inequality Measures of Age Sex Distribution
6.6 Results and Discussion
6.7 Conclusion and Recommendations

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7.1 Introduction
7.2 Objectives
7.3 About the Data
7.4 Methodology
7.5 Results and Discussion
7.6 Conclusion and Recommendations

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8.1 Introduction
8.2 Comparison of the Three models
8.3 The Amended Davidson Model
8.4 Recommendations for Further Research

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