A random variable X is said to follow a lognormal distribution if Y = log(X) follows a %3D normal distribution. The lognormal is sometimes used as a model for heavy-tailed skewed distributions. a) Calculate the density function of the lognormal distribution. b) Examine whether the lognormal roughly fits the following data (Robson 1929), which are the dorsal lengths in millimeters of taxonomically distinct octopods. (Using R) data <- c(110,15,60,54,19,115,73,190,57,43,44,18,37,43,55,19,23,82,175,50,80,65,63, 36,16,10,17,52,43,70,22,95,20,41,17,15,12,11,29,29,61,22,40,17,26,30,16,

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A random variable X is said to follow a lognormal distribution if Y = log(X) follows a
normal distribution. The lognormal is sometimes used as a model for heavy-tailed skewed
distributions.
a)
Calculate the density function of the lognormal distribution.
b) Examine whether the lognormal roughly fits the following data (Robson 1929), which are the dorsal
lengths in millimeters of taxonomically distinct octopods. (Using R)
data <- c(110,15,60,54, 19,115,73,190,57,43,44,18,37,43,55,19,23,82,175,50,80,65,63,
36,16,10,17,52,43,70,22,95,20,41,17,15,12,11,29,29,61,22,40,17,26,30,16,
116,28,32,33,29,27,16,55,8,11,49,82,85,20,67,27,44,16,6,35,17,26,32,76,
150,21,5,6,51,75,23,29,64,22,47,9,10,28,18,84,52,130,50,45,12,21,73)
Transcribed Image Text:A random variable X is said to follow a lognormal distribution if Y = log(X) follows a normal distribution. The lognormal is sometimes used as a model for heavy-tailed skewed distributions. a) Calculate the density function of the lognormal distribution. b) Examine whether the lognormal roughly fits the following data (Robson 1929), which are the dorsal lengths in millimeters of taxonomically distinct octopods. (Using R) data <- c(110,15,60,54, 19,115,73,190,57,43,44,18,37,43,55,19,23,82,175,50,80,65,63, 36,16,10,17,52,43,70,22,95,20,41,17,15,12,11,29,29,61,22,40,17,26,30,16, 116,28,32,33,29,27,16,55,8,11,49,82,85,20,67,27,44,16,6,35,17,26,32,76, 150,21,5,6,51,75,23,29,64,22,47,9,10,28,18,84,52,130,50,45,12,21,73)
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