*Appendix B.2*

We estimate per-capita incomes (US\$) of all sample families on assumption of climate change impacts and draw the distribution of the estimated incomes assuming that the distribution follows log normal distribution. To draw log normal distribution, we have to find mean and standard deviation of *ln*(*x*). Firstly, we divide the per capita income in different class and make the average (*x*) of each class and we find the frequency of household (*n*) in each per-capita income class. Then we find the log of average per-capita class, log (*x*); and multiplied by the frequency of household in each class, *n* \* log (*x*). Next average,

$$\mu = \frac{\sum n \{\log(x)\}}{\sum n} \tag{A5}$$

Then we estimate, log(*x*) − *u*, {log(*x*) − *u*}<sup>2</sup> and *n*{log(*x*) − μ}<sup>2</sup> Next standard deviation,

$$
\sigma = \sqrt{\frac{\sum n \left\{ \log(x) - u \right\}^2}{\sum n}} \tag{A6}
$$

Returns the lognormal distribution of *x*, where ln (*x*) is normally distributed with parameters Mean and Standard deviation. Use this function to analyze data that has been logarithmically transformed.

$$\begin{split} f\_{\mathbf{X}}(\mathbf{x}) &= \ \frac{1}{d\mathbf{x}} \text{Pr}(X \le \mathbf{x}) \ = \ \frac{1}{d\mathbf{x}} \text{Pr}(\ln X \le \ln \mathbf{x}) = \ \frac{1}{d\mathbf{x}} \Phi\left(\frac{\ln x - \mu}{\sigma}\right) = \ \Phi\left(\frac{\ln x - \mu}{\sigma}\right) \ \frac{1}{d\mathbf{x}} \left(\frac{\ln x - \mu}{\sigma}\right) \\ &= \ \Phi\left(\frac{\ln x - \mu}{\sigma}\right) \ \frac{1}{d\mathbf{x}} = \ \frac{1}{\mathbf{x}} \cdot \frac{1}{\sigma\sqrt{2\pi}} \exp\left(-\frac{(\ln x - \mu)^2}{2\sigma^2}\right) \end{split} \tag{A7}$$

Syntax: LOGNORM.DIST(*<sup>x</sup>*, mean, standard deviation and cumulative)
