**Estimation of return period of floods in Victoria**

### Based on data from Bureau of metEorology

Floods and drought situations have been always a major area of concern for Victoria. Some of the notable floods were in 1863, 1869, 1891 and then 1909, 1934, 1956, 1970 and 2010, 2011 and 2012. Although the fatalities were controlled but still had a very severe impacts for example Flood in 1934 (36 deaths, 6000 homeless and 400+ buildings damaged), 2010 Victorian flood (around 18 towns severely affected, 250 houses evacuated in one day, around 35 rivers were both fast and slow flooded), 2011 Victorian floods (51 affected communities, 1730 properties were flooded, total property damage of $2 Billions).

*The project was conducted to answer the following questions:*

- Question 1: How is parametric copula implemented in finding the joint marginal distributions of the two variables?
- Question 2: How does SPI utilized to study the return periods?
- Question 3: What are the best-fitted distributions for the variables?
- Question 4: What are the best-fitted copula for the joint distribution function?

When it comes to a statistical analysis, its importance in this area is increasing due to the unpredictable climatic and rainfall conditions. The rainfall characteristics for calculating the return period is multidimensional and hence requires a multivariate modelling techniques. The major requirement of conducting a multivariate or we can say bivariate in this case as the variables are 2, Severity and duration, is the fact that both the variables should be of same family of marginal density function (H. Vittala, 2015). Introduction of copula based analysis has paved a way to perform a more accurate analysis of these models as we don’t need to work on the assumptions of the variables having the same distribution. It joins different marginal distribution types to create a model and predicts the return period.