Probability density functions and expectation curves

It is common practice within oil companies to use expectation curves to express ranges of uncertainty. The relationship between probability density functions and expectation curves is a simple one. 

If the value on the x-axis were continuous rather than split into discrete ranges, the discrete PDF could be represented by a continuous function. This is useful in predicting 

For oilfield use, the x-axis on expectation curves is typically the STOIIP, GIIP, UR, or Reserves of a field. 

Expectation curves are alternatively known as probability curves . This text will use the term expectation curve for conciseness. 

The slope of the expectation curve indicates the range of uncertainty In the parameter presented a broad expectation curve represents a large range of uncertainty, and a steep expectation curve represents a field with little uncertainty (typical of fields which have much appraisal data, or production history). 

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