strata.distr: Stratification of Univariate Survey Population Using the...

In stratifyR: Optimal Stratification of Univariate Populations

Stratification of Univariate Survey Population Using the Distribution

Description

This function takes in the underlying hypothetical distribution and its parameter(s) of the survey variable, the initial value and the range of the population, the fixed sample size (n) and the fixed population size (N) to compute the optimum stratum boundaries (OSB) for a given number of strata (L), optimum sample sizes (nh), etc. The main idea used is from Khan et al. (2008) whereby the problem of stratification is fromulated into a Mathematical Programming Problem (MPP) using the best-fit frequency distribution and its parameter estimates of the data. This MPP is then solved for the optimal solutions using the Dynamic Programming (DP) solution procedure.

Usage

strata.distr(
  h,
  initval,
  dist,
  distr = c("pareto", "triangle", "rtriangle", "weibull", "gamma", "exp", "unif", "norm",
    "lnorm", "cauchy"),
  params = c(shape = 0, scale = 0, rate = 0, gamma = 0, location = 0, mean = 0, sd = 0,
    meanlog = 0, sdlog = 0, min = 0, max = 0, mode = 0),
  n,
  N,
  cost = FALSE,
  ch = NULL,
  method = c("dp", "cobyla", "global"),
  n_starts = 20L,
  max_iter = 2000L,
  tol = 1e-09,
  verbose = FALSE
)

Arguments

h	A numeric: denotes the number of strata to be created.
initval	A numeric: denotes the initial value of the population.
dist	A numeric: denotes distance (or range) of the population.
distr	A character: denotes the name of the distribution that characterizes the population.
params	A list: contains the values of all parameters of the distribution.
n	A numeric: denotes the fixed total sample size.
N	A numeric: denotes the fixed total population size.
cost	A logical: has default cost=FALSE. If it is a stratum-cost problem, cost=TRUE, with which one must provide the Ch parameter.
ch	A numeric: denotes a vector of stratum costs.
method	Character. Optimisation method: "cobyla" (fast multi-start COBYLA, default), "dp" (original Dynamic Programming solver), or "global" (exhaustive global search).
n_starts	Integer. Number of random restarts for the COBYLA solver. Default 20L. Ignored when method = "dp".
max_iter	Integer. Maximum function evaluations per COBYLA start. Default 2000L.
tol	Numeric. Convergence tolerance for COBYLA. Default 1e-9.
verbose	Logical. Print per-start progress. Default FALSE.

Value

strata.distr returns Optimum Strata Boundaries (OSB), stratum weights (Wh), stratum costs (Ch), stratum variances (Vh), Optimum Sample Sizes (nh), stratum population sizes (Nh).

Author(s)

Karuna Reddy <[e-mail]>
MGM Khan <[e-mail]>

See Also

strata.data

Examples

## Not run: 
#Assume data has initial value of 1.5, distance of 33 and follows
#weibull distribution with estimated parameters as shape=2.15 and scale=13.5
#To compute the OSB, OSS, etc. with fixed sample n=500, we use:
res <- strata.distr(h=2, initval=1.5, dist=33, distr = "weibull",
params = c(shape=2.15, scale=13.5), n=500, N=2000, cost=FALSE)
summary(res)
#-------------------------------------------------------------
#Assume data has initial value of 1, distance of 10415 and follows
#lnorm distribution with estimated parameters as meanlog=5.5 and sdlog=1.5
#To compute the OSB, OSS, etc. with fixed sample n=500, we use:
res <- strata.distr(h=2, initval=1, dist=10415, distr = "lnorm",
params = c(meanlog=5.5, sdlog=1.5), n=500, N=12000)
summary(res)
#-------------------------------------------------------------
#Assume data has initial value of 2, distance of 68 and follows
#gamma distribution with estimated parameters as shape=3.8 and rate=0.55
#To compute the OSB, OSS, etc. with fixed sample n=500, we use:
res <- strata.distr(h=2, initval=0.65, dist=68, distr = "gamma",
params = c(shape=3.8, rate=0.55), n=500, N=10000)
summary(res)
#-------------------------------------------------------------
#The function be dynamically used to visualize the the strata boundaries, 
#for 2 strata, over the density (or observations) of the "mag" variable 
#from the quakes data (with purrr and ggplot2 packages loaded).
res <- strata.distr(h=2, initval=4, dist=2.4, distr = "lnorm", 
          params = c(meanlog=1.52681032, sdlog=0.08503554), n=300, N=1000)
quakes %>% 
      ggplot(aes(x = mag)) +
      geom_density(fill = "blue", colour = "black", alpha = 0.3) +
      geom_vline(xintercept = res$OSB, linetype = "dotted", color = "red")
#-------------------------------------------------------------

## End(Not run)

stratifyR documentation built on Sept. 10, 2026, 5:07 p.m.