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I have fitted a mixture of 3 normal distributions to my log-transformed data Y, as the package I'm using cannot fit a mixture of lognormal distributions.

My questions is: how I can convert pdf from 3 normal distributions into lognormal pdf?

Thank you.

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It is just the same mixture of the associated log-normal PDFs. Your mixture model says that $\log Y|\mu \sim N(\mu,\sigma^2)$, so $Y|\mu$ has a log normal distribution. The distribution of $\mu$ (a discrete distribution on 3 values) is the same.

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