From CPI and PPI, which is better to calculate inflation?

As the CPI does not include rural or non-metropolitan areas, farm families, people in the armed forces and those in institutions such as prisons and mental hospitals, the U.S. Bureau of Labor Statistics (BLS) uses additional indexes to measure inflation. The producer price index(PPI) which measures the domestic output of raw goods and services, serves as a leading indicator for the CPI; when producers face input inflation, the increase in their production costs are passed on to the retailers and consumers. Hence, the PPI serves as a true measure of output; it is not affected by consumer demand. The gross domestic product (GDP) deflatormeasures the aggregate prices of all goods and services produced by the entire nation encompassing the CPI and the PPI statistics. The CPI is a sound index to measure inflation, but for a more accurate and comprehensive measure, the PPI and the GDP deflator are also required.