O IDHM é obtido pela média geométrica dos três subíndices das dimensões que compõem o índice: longevidade, educação e renda.

Longevity Dimension

Long and Healthy Life

In the MHDI, this dimension is measured by the life expectancy at birth.

What does the MHDI Longevity consist of?
The MHDI Longevity dimension considers the life expectancy at birth, in other words, the average number of that people are expected to live at the moment of birth, in the municipalities, Federal Units (UF), Metropolitan Regions (RM) or Human Development Units (UDH), while maintaining the same mortality patterns observed in each period.
What does this indicator measure?
Life expectancy at birth can be considered as an indicator of longevity, as it summarizes the level and structure of mortality within population a single number.
Why this indicator?
Life expectancy at birth summarizes the social, health and general municipal well-being conditions in order to examine the mortality rates of different age groups in the area. In order to calculate this indicator, all death causes are taken into consideration - diseases as well as external causes, such as accidents and violence.
How is this indicator calculated?

The suggested demographic indicators in Atlas of Human Development I n Brazil - including life expectancy at birth - cannot be obtained directly from information in Demographic Censuses - thus, indirect techniques are used.

These methods - the technique for calculating the mortality rate of children and young people, the indicators of longevity and mortality, as well as the technique to calculate the total estimated fertility rate in total - were developed by William Brass (1968).

However, it should be noted that the techniques used required some adjustments for application in locations with small populations, such as in many municipalities or areas within municipalities. This adaptation was made by Professor José Alberto Magno de Carvalho, from the Center for Regional Development and Planning of (CEDEPLAR), at the Federal University of Minas Gerais (UFMG).

Furthermore, applying the methodology requires a standard mortality function. Ideally, it would be known as the mortality pattern of the particular population. When it is unknown, we use standard mortality tables or a mortality table for a given population, whose mortality pattern is considered similar to that of the population of the study. When calculating the mortality rates, especially for the Brazilian municipalities and UDH's, the output tables were used as a standard for levels of aggregation for their respective states.

The mortality tables for 1991 and 2000 were based on the Demographic Census of 1991 and on the National Research by Household Sample (PNAD) of the 1990s. These mortality tables for Brazilian states, developed by CEDEPLAR, were used as the standard. The tables that already included the results of the Demographic Census of 2010, estimated by CEDEPLAR, were also adopted for 2010

The main limitation of this indicator arises from the fact that the mortality standards of the municipalities are unknown. This gap was filled by adopting the mortality pattern of the state for each municipality, as determined by survival tables that CEDEPLAR/UFMG has developed for each federative unit of the country. It is recognized that this is a non-trivial assumption. The same disparities indicated by the survival tables must occur within each state, because the interregional inequalities in the country are also reproduced at the state level.
Weight of Variables
In the overall index, there is only one variable with a weight of 1.
Comparison and Adjustments with the Global HDI
MHDI Longevity examines the same indicator as the global HDI.
Source of Information
IBGE Demographic Census
Since 1970, the statistics of the Demographic Censuses has enabled the use of the Brass’s technique, providing the necessary information to calculate fertility indicators: live births during the 12 months preceding the date of the Census (current fertility), total of live births (retrospective fertility or parturition) and mortality (total of live births and total of children at the date of the Census) by the age range of women.
Support indicators in analyzing MHDI Longevity Dimension
Two blocks of Atlas of Human Development in Brazil indicators can be used as a proxy for the evaluation of health conditions. The first block consists of longevity and mortality indicators, including the infant mortality rate, the odds of death within 5, 40 and 60 years of age and life expectancy at birth. The second block consists of the total fertility rate. The infant mortality rate is one of the most significant indicators, because it reflects the impact of socioeconomic conditions of the geographical location where the child is born. The more developed a region is - the more closely related the infant mortality rate is to the endogenous causes determined by the risks of newborn mortality (first 28 days of life). In less developed regions, in addition to endogenous causes, the exogenous causes - including malnutrition and infectious and respiratory diseases – add up decisively. The probabilities of demise reflect deprivation at different stages of life, in which different causes have negative effects. The behaviour of the total fertility rate is linked to the changes the Brazilian population has gone through in the so-called demographic transition, during which the rapid decline of fertility levels determined the population volume and the new, national configuration, in terms of age structure.
How is the MHDI Longevity Dimension calculated?
The process of transforming the life expectancy at birth indicator, whose unit is "years of life", into the Index of Longevity, requires that we select the maximum and minimum parameters to normalize the indicator, using the following formula:
I = (observed value - minimum value) / (maximum value - minimum value).

The same maximum and minimum values were also adopted in the previous editions of MHDI:
• Maximum age: 85 years • Minimum age: 25 years

Thus, e.g.,
If the life expectancy of a municipality is 70 years, its MHDI Longevity would be: (70 – 25) / (85 – 25) = 45 / 60 => MHDI Longevity = 0,750.