Method of moments estimates and likelihood from a lognormal distribution

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Sunny95

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Let X1, . . . , Xn be an i.i.d. sample from a lognormal distribution with parameters µ and σ. The lognormal density isf(x | µ, σ) = 1xσ√2πexp −(log x − µ)22σ2, x > 0.Moreover, the (natural) logarithm of a lognormal random variable with parameters µ and σ isnormally distributed with mean µ and variance σ2.
1. Find the method of moments estimates of µ and σ.
2. Find the mle’s of µ and σ.
I need help with these 2 question!
 
Sunny95 said:
Let X1, . . . , Xn be an i.i.d. sample from a lognormal distribution with parameters µ and σ. The lognormal density isf(x | µ, σ) = 1xσ√2πexp −(log x − µ)22σ2, x > 0.Moreover, the (natural) logarithm of a lognormal random variable with parameters µ and σ isnormally distributed with mean µ and variance σ2.
1. Find the method of moments estimates of µ and σ.
2. Find the mle’s of µ and σ.
I need help with these 2 question!
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What are your thoughts, based on what you've learned in class and from your textbook? What have you tried? How far have you gotten? Where are you getting stuck?

Please be complete. Thank you! ;)
 
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