Statistics & Demography

the distribution of the individuals in the population across designated categories; esp. age and sex

the growth or decline in the size of the population or its component parts over time

the number of individuals resident per unit area of territory

the number of offspring produced by an individual in a given time interval

the likelihood of death occuring to an individual in a given time interval

the proportion of individuals entering or leaving a population, other than through fertility or mortality

the derivative of the function Z with respect to x

any symbol with a bar over it is an average value

any primed symbol indicates a data value (rather than a life table value)

any symbol with a hat over it is to be expressed in decimals (usually implying percents)

the logarithm of the base e; the natural logarithm

any starred symbol indicates a modified value (such as to account for both sexes, express a hypothetical maximum etc)

any symbol with a v-hat over it indicates a temporary working value which must be modified before it can be used

a group of individuals who are the same age, or within the same predetermined age range

the root of the life table, generally arbitrarily defined as 1.0 or some power of 10

the annual birth cohort size in general

average age of adults in a population

average age in population

Crude birth rate; the number of births per person per year

age specific fertility rate; chance of a person x years old giving birth to offspring of the same sex

average of age-specific fertility values

Gompertz function graduation coefficients

Age distribution; percent of the population age x

percent of the population between the ages a and b

Age distribution; fraction of the population in age class X

Crude death rate; number of deaths per person per year

Dependency ratio: number of dependents per productive adult

the number of dependents, both juvenile and elderly, per productive adult

base of natural logirithm

life expectancy at age x

average number of live births per female reaching menarche; average family size

Age-specific birth rates for age class X; life table notation to signify that the rates are for same sex birth only

Index of Growth Regulation

Gross reproductive rate; completed family size

Index of Growth Regulation

Relative coefficient for age-specific fertility rate in age class X

K(X) coefficients used in constructing models

number of survivors to age x out of a radix l(0)

chance of survivorship from birth to age x

person-years lived in age class X; also sum of survivors, l(x), in that class

person-years lived in age class based on unit radix, that is, the sum of l-hat(x) in class

age class width in years

population size

census count in age class from age x to x+n

net reproductive rate, R-sub-o

probability of surviving from age x to age n + x

probability of dying between age x and age x + n, equal to 1 - sub-n p sub-x

answer

probability of dying in X age class for those reaching age X

intrinsic growth rate of population size per year

net reproductive rate; sum of phi (x)

chance of surviving from age 15 to 50 (or other arbitrarily assigned range of adulthood)

sex ratio of the population age x

total sex ratio of the population

generation length

years to be lived by total population now aged X, before all are dead, in person-years

age

midpoint of age class: X + (n/2)

age class beginning at age X; used for denoting values taken on in the age class, and for the age class itself

age of menarche (usually arbitrarily 15)

age of menopause (usually arbitrarily 50)

Index of Dissimilarity (change)

sex ratio at birth

rate of infanticide; generally sex is specified with subscript m or f

instantaneous rate of mortality at exactly age x

factory by which fertility must change for population to go from zero growth rate to r growth rate

net maternity function; product of survivorship and fertility at age x

oldest age which can be attained before death

D/(P(t)) Crude death rate = number of deaths/ (population size x time period during whichdeaths occur)

D sub-x/ (P sub-x) t, or Number of deaths at age x, divided by the product of the population at age x and the time period

age-specific probability of death

survivorship for each age category; probability that an individual from the hypothetical birth cohort is still alive at the start of the age

d of x = l of x (q of x)

number of years that an average person will live in an age interval

total person-years of life remaining to the cohort of individuals entering the age interval

T of x / l of x, or total life years remaining to a person entering age x, time age-specific survivorship

age-specific deaths

population in which vital rates, relative age distribution, and census counts are all constant

population in which the rate of growth does not change

the instantaneous risk of death as a continuous function of time

Survivor function; probability that an individual survives to at least time t

Probability Density Function of T; expresses the instantaneous rate of change of the Survivor Function

the Probability Density Function divided by the Survivor Function

q of x or - (1/(S(t))) x ((d/dt)S(t))