Constant and variable hazard functions.

Abstract

<p>(A) Two different gamma densities of the time <i>T</i> at which the critic receives notification of an impending lever press. (B) Corresponding hazard functions <math><mrow><mi>h</mi><mrow><mo>(</mo><mi>t</mi><mo>^</mo><mo>)</mo></mrow><mo>=</mo><msub><mo>lim</mo><mrow><mo>Δ</mo><mi>t</mi><mo>^</mo><mo>→</mo><mn>0</mn></mrow></msub><mrow><mo>{</mo><mi>P</mi><mrow><mo>(</mo><mi>T</mi><mo>≤</mo><mi>t</mi><mo>^</mo><mo>+</mo><mo>Δ</mo><mi>t</mi><mo>^</mo><mo>|</mo><mi>T</mi><mo>></mo><mi>t</mi><mo>^</mo><mo>)</mo></mrow><mo>/</mo><mo>Δ</mo><mi>t</mi><mo>^</mo><mo>}</mo></mrow></mrow></math>. Note that the hazard function is constant in the <math><mrow><mi>G</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>)</mo></mrow></math> case, but increases with time in the <math><mrow><mi>G</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>1</mn><mo>)</mo></mrow></math> case.</p