exponential

survival.exponential(rate)

Exponential survival curve with a constant hazard.

The special case of weibull with shape=1, kept as its own family because a constant hazard has a closed-form discounted life expectancy, 1 / (discount_rate + rate), used to check heormodel.survival.algebra.apply_hazard_ratio.

Parameters

Name	Type	Description	Default
rate	`float`	Constant hazard (events per year). Must be positive.	required

Returns

Name	Type	Description
	SurvivalCurve	A `SurvivalCurve` with `survival(t) = exp(-rate * t)`.

Example

from heormodel.survival import exponential curve = exponential(rate=0.2) round(float(curve.survival(5.0)), 5) 0.36788

# exponential { #heormodel.survival.exponential }

```python
survival.exponential(rate)
```

Exponential survival curve with a constant hazard.

The special case of `weibull` with `shape=1`, kept as its own family
because a constant hazard has a closed-form discounted life expectancy,
`1 / (discount_rate + rate)`, used to check `heormodel.survival.algebra.apply_hazard_ratio`.

## Parameters {.doc-section .doc-section-parameters}

| Name   | Type             | Description                                          | Default    |
|--------|------------------|------------------------------------------------------|------------|
| rate   | [float](`float`) | Constant hazard (events per year). Must be positive. | _required_ |

## Returns {.doc-section .doc-section-returns}

| Name   | Type                                                      | Description                                            |
|--------|-----------------------------------------------------------|--------------------------------------------------------|
|        | [SurvivalCurve](`heormodel.survival.curve.SurvivalCurve`) | A `SurvivalCurve` with `survival(t) = exp(-rate * t)`. |

## Example {.doc-section .doc-section-example}

>>> from heormodel.survival import exponential
>>> curve = exponential(rate=0.2)
>>> round(float(curve.survival(5.0)), 5)
0.36788