The pattern of varies from society to society according to the customs and
social norms of the society concerned. In fact, the age associated with marriage
provides an idea about the social contact and it has become a subject of interest
among social scientists. Researchers involved with the study of the special
pattern of the society have been giving the more attention to the marriage field
emphasizing it is relationship between marriage and associated age difference.
A verity of models has been development to study of age associated with marriage
in India and others parts of the world during the last few decades[1-7].
Sharma proposed a probability model to describe the distribution of age associated
with marriage for Northern India based on the assumption (i) the distribution
of marriages being uniform up to a certain age (say) D. The number of marriages
is proportional to the area of the age difference interval d1 to
d2. The number of marriages with age interval (d1<d2<D)
is proportional to . And (ii) after the age difference D in a particular
direction, the distribution of age as follows an exponential form that is the
number of marriages in the interval d1 to d2 (D<d1<d2)
Where λ is the risk parameter. The concept behind taking this model was that the age factor is immaterial up to a certain age and marriages are arranged without giving due to consideration to the age. After that particular age as mentioned above the marriage probabilities will be a decaying function of the age keeping in mind the Hindu society involved in the process. Abedin et al. extended the model proposed by Sharma as follows:
If M is the number of marriages at age x; then
This model provided a better an approximation as compared to the Sharmas
model. It should however, be noted that the above models for the age associated
with marriage have been proposed/developed keeping in mind the Hindu society
involved in the process. In a Hindu society, most of the marriages usually take
15 to 20 for male and women take (10-18). All the boys and girls of a village
are related as brothers and sisters. 2.3% boys and girls are marriage with teen-age
there relations. The problems that arise in marriage and family
life apparently have not discouraged persons from entering into such relationships.
As a matter of fact, more people are marring today than 20 years ago. In 1998
it was found that 7.8% of all males and 7.02% of all females 35 and over married.
Only, 1.02% people had never married.
The age at which people are marrying has also been changing. The first half of this country should a steady decline in the boyhood age at first marriage. This trend is continued until the1971s and 1981s.
After varying periods of unhappiness and readjustment most divorced persons
eventually remarry and the likelihood of this second marriages proving successful
is almost as great as that for first. Therefore the models proposed by Sharma
and Abedin et al. are not suitable to describe the marriage
age of Muslim society. Fortunately, a set of data is an available from a sample
survey entitled Impact of migration on fertility in Bangladesh: A study
of Dinajpur district. The Dinajpur district is bounded on the south by Joypurhat
zilla and north by Thakurgoan and on the east Rangpur, Gaibandha, Kurigram district.
It is one of the oldest districts of Bangladesh. The cluster survey sampling
methodology adapted for the selection of sample. A total 2686 sample household
from 10 clusters has been interviewed. A study of Dinajpur district survey can
be seen in Hossain. Hossain tried to fit the models mentioned
earlier. This model did not provide a good fit and Hossain than
applied the pareto-exponential function proposed by Morril and Pitts
to describe the age difference associate with marriage for this data of Bangladesh.
Through this model is provided better approximation than the models proposed
by Sharma and Abedin et al. but still did
not adequately fit the data set utilized. It seems that a model to describe
the distribution of age associated with marriage in a Muslim community should
be based on the assumption that the number of marriages is a decaying function
of age i.e. age increases the number of marriages tendency decreases.
Exponential distribution may be a good example for this situation and it is
proposed in this study.
Pareto-Exponential Function: Abedin applied Morril
and Pittss model to study age associated with marriage on
the data of Bangladesh. In brief this model is if Y is the number of marriages,
X is the age associated with marriage then Pareto-Exponential Function
may be expressed as follows:
Where a, b and c are the parameters. Taking logarithms on both sides of the
above equation, the equations take the linear form:
|| Distribution of the age associated with marriage for different
marriage cohorts, Dinajpur, Bangladesh
|Exp. M.A. = Exponential distribution of marriage A of the
Exp. M.B. = Exponential distribution of marriage B of the Hindu community
d.f. = Decay function
The parameters a, b and c can easily be estimated from equation (5) using the methods of least squares.
Exponential distribution: Due to the reasons as pointed out above the
number of marriages at different ages in Muslim community may be a decaying
function of age i.e. the number of marriages tends to fall quite rapidly
for higher ages. Consequently exponential distribution may appear to be a suitable
on to describe the age associated with marriage. Suppose, P denote the age associated
with the marriage then the probability density function of X is follows:
Where θ is the risk parameter. Then the cumulative distribution function
of females getting married at age less than or equal to p is given by:
This distribution contains only one parameter θ, which is to be estimated.
The maximum likelihood estimate of θ is given by:
is the observed sample mean age associated with the marriage.
Application: Both the pareto-exponential and exponential models are applied to the data of Bangladesh for different marriage cohorts as taken by Abedin. Table 1 shows the number of marriages according to the age in different marriage cohorts. It was found that the pareto-exponential model suitably describe the data for the marriage cohort before 1971-1981 and 1981- 1991 but did not fit well for the marriage cohorts 1991-1997 whereas the exponential model was found suitable the data sets. Thus a better fit of the age associated with the marriage, particularly for marriages of Muslim community could be obtained by the exponential distribution as compared to the pareto-exponential function as applied by the Abedin.
In this study the distribution of the age associated with marriage has been studied using pareto-exponential function and the exponential distribution. The finding indicated that the exponential distribution provides a better approximation to the distribution of age associate with Muslim community.