Recent content by user1234

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    "Number of Persons” Vs “Number of Person-years” in a Stationary Population

    I have learnt that the life table function nLx is the number of "person-years" lived by the cohort between ages x and x+n. But for stationary population, nLx is defined as the number of persons in the population who at any moment are living within the age interval (x, x+n). I don't...
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    Concept of Stationary Population in Demography.

    Thank you so much for making it clear to me. In real life, is it usual to have same age-specific probabilities of death over time? I suppose so. Because if no war or epidemic happens, then the age-specific probabilities of death can be same year to year. Am I wrong? Is the assumption of same...
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    Concept of Stationary Population in Demography.

    The definition of stationary population is: "The stationary population is a model without immigration or emigration in which the same age-specific probabilities of death apply continuously and in which there are the same number of births and deaths each year." Can anyone please explain me...
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    What is the reason behind getting unbiased and efficient estimator by ranked set samp

    In ranked set sampling (RSS), we select n random sets, each of size n. Then we choose the largest unit from the 1st set, 2nd largest from the 2nd set, and thus n th largest from the n th set for the actual measurement. What is the intuition that a sample thus obtained will give an unbiased...
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    Relative Efficiency

    Consider the following equation: T_i = A_i + Z_i * B_i,i=1,2...,6. Suppose for all i(i=1,2,...,6) data generation of A_i and B_i are exactly same for two methods. The two methods differ only in generating data of Z_i. For method 1, Z_i is generated from Bernoulli distribution with...
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    Checking significance of bias.

    In a new design, estimator seems to be biased but efficient than the existing design. Now I want to check whether the bias of the estimator based on new design is significant. The formula of the variance of the estimator based on new design is intractable. How can I check the...
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    Efficient R coding

    Consider the following data frame: dat <- data.frame(x=c(0,128.96,0,397.37,56.80,0,801.79,340.79), y=c(40,97,172,186,210,246,327,432), d=c(1,0,0,0,0,1,0,1), A=c(0,1,0,1,1,0,1,1), B=c(0,1,0,1,1,0,1,1)) For each value of the column y which satisfies...
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    difference between estimating variance and standard deviation.

    In a simulation study, is there any difference between \bullet to estimate the variance \sigma^2, 1000 times and taking its average, and \bullet to estimate the standard deviation \sigma, 1000 times and taking its average? Can I do anyone of these? Is there any preference of doing a...
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    Rewriting integration by summation

    Suppose that n individuals have lifetimes represented by random variables T_1, T_2, \ldots, T_n. Instead of the observed values for each lifetime, we have a time t_i' which we know is either the lifetime or censoring time. Let us define a variable \delta_i=I(T_i=t_i') that equals 1 if...
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    probability for two replication

    Suppose that a sample of size n is to be chosen randomly (without replacement) from an urn containing N balls, of which m are white and N-m are black. If we let X denote the number of white balls selected, then the probability of getting exactly i white balls is...
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    For the following example, is order meaningful or not?

    Consider a hypothetical example. There are 12 tickets for a documentary film and exactly 12 people to buy the tickets (one person can buy only one ticket). There are 3 ticketbooths for selling the tickets and each ticketbooth will sell exactly 4 tickets. Suppose the researcher labels the 12...