A sample is drawn from Gamma(k, 0) population, where k> 0 is known (given) is the...

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A sample is drawn from Gamma(k, 0) population, where k> 0 is known (given) is the shape parameter, and 0> 0 is unknown, and called the scale parameter. The gamma distribution with these parameters is given by the density { Here, I'(k) is the gamma function (not to be confused with gamma distribution). Create an R function MLEtheta (xsample, k) which for a sample xsample from Gamma(k, 0) population (where xsample is an arbitrary R numeric vector with positive values) and for the given (known) value k> 0 of the shape parameter, gives the maximum likelihood estimate for the parameter 0. f(x; k, 0) = -xk-le- I'(k) ok 0 ,x>0 , elsewhere Side Note: Apart from the scale parameter 0, another parameter 1, called rate parameter, can be specified instead of the scale parameter 0. These two parameters are closely related: 0 = 1. The rate is average frequency/rate of arrivals of so called Poisson events; the distribution Gamma(k, 0 = D ) can arrivals per unit time, and average time 0 = 1 between two Poisson arrivals. then be interpreted as a waiting time of the k-th Poisson arrival, with an of Here, k is generalized from any natural number to any positive number. A sample is drawn from Gamma(k, 0) population, where k> 0 is known (given) is the shape parameter, and 0> 0 is unknown, and called the scale parameter. The gamma distribution with these parameters is given by the density { Here, I'(k) is the gamma function (not to be confused with gamma distribution). Create an R function MLEtheta (xsample, k) which for a sample xsample from Gamma(k, 0) population (where xsample is an arbitrary R numeric vector with positive values) and for the given (known) value k> 0 of the shape parameter, gives the maximum likelihood estimate for the parameter 0. f(x; k, 0) = -xk-le- I'(k) ok 0 ,x>0 , elsewhere Side Note: Apart from the scale parameter 0, another parameter 1, called rate parameter, can be specified instead of the scale parameter 0. These two parameters are closely related: 0 = 1. The rate is average frequency/rate of arrivals of so called Poisson events; the distribution Gamma(k, 0 = D ) can arrivals per unit time, and average time 0 = 1 between two Poisson arrivals. then be interpreted as a waiting time of the k-th Poisson arrival, with an of Here, k is generalized from any natural number to any positive number.

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Likelihood function 10 I Lo... View the full answer