Estimates of fecundability from a truncated distribution of conception times

A population consisting of women who have conceived before a time t ignores all women whose conception time exceeds t. Such a population is considered as a truncated population, and the samples are called truncated samples. Under the assumption that fecundability among women varies according to a Beta distribution (with parameters a and b), the distribution of conception times in a truncated population can be considered as truncated Type I geometric. This paper presents an algorithm to obtain the moment and maximum likelihood estimates of a and b from the truncated samples. Large sample properties of the estimators are also studied. Examples using the Hutterite and the Princeton Fertility Survey data are given.     

A modification of a continuous time model for first conception

The interval between marriage and the first conception leading to a live birth plays an important role in the determination of fertility components. Several probability models (Potter and Parker, 1964; Singh, 1961, 1964, 1967) based on varying sets of assumptions relating to this interval have been propounded in the recent past. All of them are based on the assumption that the females under study are susceptible to conception at the time of marriage. However, in certain situations, where some of the females already pregnant at the time of marriage report to have conceived within a short interval following marriage, this condition is not satisfied and these models become unsuitable. A probability distribution which is an inflated form of the continuous model proposed by Singh, for the time of the first conception leading to a live birth, is presented in this paper. It describes reasonably well the data on first conception times in the context of premarital conceptions. Simple expressions for the maximum likelihood estimators of the parameters involved in the model are obtained and a method for finding the asymptotic covariance matrix of the estimators is outlined. The model is applied to four sets of data.     

Serious imbalance of population distribution in Beijing: Population density in core areas a hundred times that in outer suburbs

According to the data released by the Leading Group Office of the Sixth National Population Census of Beijing, 79.5% of Beijing’s population is concentrated in urban function-expansion areas or new urban     

Sex selection and fertility in a dynamic model of conception and abortion

This paper investigates the effect of prenatal sex selection on fertility through a stochastic dynamic model with uncertainty in conception as well as in gender, where a woman makes decisions on conception and abortion with or without gender detection tests (i.e. sex-selective or sex-unselective abortion). The paper shows that, when the cost of gender detection test falls, the sex ratio at birth rises due to more selective abortions, but fertility can rise or fall with rising sex ratio. Fertility may rise (fall) if there are more (less) women giving up unselective abortions for selective abortions than women giving up childbirths without test for selective abortions. Similarly the paper shows that the sex ratio can rise or fall, when fertility decreases as the cost of children increases. I test these propositions as well as their implications against micro survey data on the pregnancy history of Korean women.Responsible editor: Junsen Zhang.     

The risk of conception on different days of the menstrual cycle

Abstract Data on 1898 menstrual cycles, for 241 married women, were analysed by means of a quantal regression programme. The locations of the day of ovulation was determined by the basal body temperature method. Estimates were obtained of the risk of conception from an act of coitus on each day, as measured from the day of ovulation. The relationship between fecundability and coital frequency was also examined.     

Estimation of stage-specific developmental times and survivorship from stage frequency data

Summary An algorithm for estimating mean stage durations, the standard deviations associated with the means, and stage-specific survivorships from stage frequency data is presented. The algorithm is based on an age-structured, distributed delay simulation model which usesErlang distributions to determine the probability of maturity for individuals in each stage. If the data set extends beyond the first generation, the algorithm requires a fecundity rate, as well as stage frequencies, as input. Goodness-of-fit was measured using a weighted least squares calculation summed over all observed stages and all sampling dates.     

Maximum likelihood estimates for the parameters of a continuous time model for first conception

The duration of time between two successive births or between marriage and first birth is an indicator of the level of fertility of a couple. Potter and Parker (1964) and Singh (1961, 1967) have suggested the Type I Geometric as a distribution appropriate for representing the length of interval to first conception leading to a live birth. Potter and Parker estimated the parameters of this distribution with the help of the first two moments. Majumdar and Sheps (1970) pointed out the limitations of these moment estimates and gave a method to obtain maximum likelihood estimates, based on formulas which are too involved for solution without the help of a computer. Singh proposed a continuous probability distribution based on another set of assumptions for the above situation. He outlined a method to obtain best asymptotically normal estimates of the parameters. These estimates are obtained after several iterations starting from any set of consistent estimates. The objective of this paper is to show that it is relatively easier to obtain maximum likelihood estimates of the parameters of the continuous model, which describes the data on duration to first conception as well as does the discrete model. Simple expressions for the moment and maximum likelihood estimates with the corresponding covariance matrices are obtained. Application is made to three sets of data.     

The geometric mean of the age-specific death rates as a summary index of mortality

Even though a single summary index of mortality can never replace the set of age-specific death rates, it has been found to be extremely useful for a wide variety of purposes. Such indexes are generally one of two types: aggregative indexes, such as directly standardized rates which reflect absolute differences between corresponding age-specific mortality rates; and average of relatives indexes which reflect proportional differences between those rates. The choice of index depends upon the purposes for which it is to be used, and is important as different indexes can produce very different results. While directly standardized rates are widely used, they depend upon the selection of an appropriate standard population and give disproportionately heavy weight to the high ages. Average of relatives indexes give equal weight to all ages, but are infrequently used as no index of that type has gained wide acceptability. This paper recommends the use of the geometric mean of the age-specific mortality rates as such an index, and shows that this index is readily calculable, unbiased, needs no standard population, is directly comparable to all other indexes so calculated, and accurately reflects exponential mortality patterns.     

A mortality model based on a mixture distribution function

A new mortality model based on a mixture distribution function is proposed. We mix a half-normal distribution with a generalization of the skew-normal distribution. As a result, we get a six-parameter distribution function that has a good fit with a wide variety of mortality patterns. This mixture model is fitted to several mortality data schedules and compared with the Siler (five-parameter) and Heligman–Pollard (eight-parameter) models. Our proposal serves as a convenient compromise between the Heligman–Pollard model (which ensures a good fit with data but is often overparameterized) and the Siler model (which is more compact but fails to capture ‘accident humps’).     

Ecological studies on a dragonfly,Nannophya pygmaea ramber (Odonata: Libellulidae) I. seasonal changes of adult population and its distribution in a habitat

Summary Adult population of a dragonflyNannophya pygmaea Ramber inhabited in a damp ground was investigated with mark-and-recapture method in 1975. The following results about the seasonal changes of the population size and distribution in the habitat were obtained. Adults emerged from late May to mid August. The number of the adults was most abundant in early June, but that of matured males in early July. From the recapture data, the estimate of daily survival rate was 0.82, and the length of immature stage in males was estimated as 5 days or so. Total number of post-teneral adults emerged in the habitat was estimated as about 9,000. The mean crowding-mean density regression method was applied for the analysis of the distribution pattern of the adults. Matured males showed a spaced-out distribution, while females and immatured males distributed themselves rather aggregatively. Such a distribution pattern of the matured male would be attributed to their territorial behaviour. The territorial behaviour was considered to force the matured males to extend the distribution area in July when they were most abundant. From the above-mentioned results and some observations, the meaning of the territoriality in this species was discussed.     

Some further observations on the index of residential differentiation

The relationship between the index of residential differentiation (RDI), a recently introduced measure of residential segregation which is designed to summarize the distribution of c social groups in a single index, and the indices of dissimilarity (D) and segregation (SI) is examined. It is demonstrated that RDI is a natural extension of D, and that when c = 2, RDI = D; when c> 2, it is possible to stipulate RDI in terms of SI, but it is not possible to stipulate RDI in a straightforward manner in terms of D. An adjusted RDI is then suggested in which random segregation rather than complete desegregation is used as the baseline.     

Summary indices of the age distribution of a population

In this paper a method for characterizing the age distribution of a population by means of an ‘index word’ is outlined. It is shown that the method can be applied to yield approximations to population forecasts.     

Some observations on The Condition of Education (1976 edition)

The Condition of Education 1976 assembles data in table and chart on a wider range of educational data than have appeared in previous Federal reports, organizing them around issues and divisions of the U.S. educational establishment. The elementary/secondary and higher education levels are more adequately represented than other system levels. Six system properties are introduced to evaluate the degree of representation in the volume: environment, structure, culture, output, throughput, and input. System output is best represented by the volume, and system culture is greatly under-represented; otherwise, the 124 educational indicators are fairly well distributed across system properties. System properties by educational level again reveal culture to be inadequately measured. Temporally, 70 of the 124 indicators are presented in more than 2 points in time but only 13 indicators are projected into the future. Utilization of this classification system reveals areas of the statistical system needing greater emphasis, particularly system demographics, properties of kindergarten/nursery, post-secondary noncollegiate, graduate/professional, and adult-education levels, a need for more indicators of cultural variables, and a need to interrelate system output with input and throughput.     

Asymptotic properties of a human age distribution under a continuous net maternity function

A useful and intuitively appealing proposition in theoretical demography asserts that the age distribution of a closed human populationis asymptotically independent of this shapein thedistant past, and is therefore exclusively determined by the historyof fertility and mortalitythat has prevailed during a reasonably long period of time. The mathematical foundations of this ergodic principle arelaid out in this article and thedetailsof its proofareworked out afteremphasizing an intuitive understanding of the process through which an age distribution tends to "forget" its past. The tendency for an unchanging schedule of vital ratesto produce a fixed agestructure in a closed population, is presented as a corollary of the main proposition dealt with in this article.     

Aging in precarious times: Exploring the role of gender in shaping views on aging

ABSTRACT

The present study explores views on aging and how these differ according to gender and precariousness status. Semistructured interviews were conducted with 10 men and 10 women with secure and insecure pensions. Themes like fear of illness and health decline were more present in men, while fear of losing their attractiveness in old age more present among women. For all participants, loss of autonomy and social roles represented a negative view of old age, while activity in the form of work, volunteering, or leisure represented positive views. Differences in views on aging were related to pension security and less to gender. Women with insecure pension plans displayed the most negative views of aging. Implications for practice and policy to prevent health and gender inequalities are discussed.     

A further note on the estimation of a fitness function from two samples taken from a popolation

Summary A modification is proposed for the moments method for estimating a fitness function that was discussed in an earlier paper (Manly, 1976b). This modification ensures that fitness estimates are always positive. The theory has been worked out for a fitness function of any number of variables and a computer program has been written to carry out the iterative calculations needed for estimation.     

Experimental studies on the distribution of the aphid counts

Summary The present paper dealt with the sequential changes of the distribution pattern of apterous females aphid populations, that were artificially settled at the beginning on the experimental barley ‘field’. The aphids were settled at random or even with a fixed denisty per plant. For five or six days after the settling, the number of individuals followed the negative binomial distributions in all cases while the parametersk andp were varying. The estimated values ofk were rather small for the first one week after the settling, which may suggest that the number of moving aphids between plants was relatively small and the degree of concentration expressing the intrinsic increase was high. After that, as the number of individuals increased, the number of moving aphids between plants would be considered to be increased. It was found that with the lapse of time the degree of concentration decreased ork became larger. The distribution of aphids per blade in a plant was also described briefly.