Binomial Distribution

stamox.distribution.pbinom(q: ArrayLike, size: ArrayLike, prob: ArrayLike, lower_tail: Bool = True, log_prob: Bool = False, dtype = <class 'jax.numpy.float64'>) -> ArrayLike

Calculates the cumulative probability of a binomial distribution.

Parameters:

Name	Type	Description	Default
q	ArrayLike	The quantiles to compute.	required
size	ArrayLike	The number of trials.	required
prob	ArrayLike	The probability of success in each trial.	required
lower_tail	Bool	If True (default), the lower tail probability is returned.	True
log_prob	Bool	If True, the logarithm of the probability is returned.	False
dtype	optional	The data type of the output array. Defaults to jnp.float_.	<class 'jax.numpy.float64'>

Returns:

Type	Description
ArrayLike	The cumulative probability of the binomial distribution.

Examples:

>>> q = jnp.array([0.1, 0.5, 0.9])
>>> size = 10
>>> prob = 0.5
>>> pbinom(q, size, prob)

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stamox.distribution.qbinom(p: ArrayLike, size: ArrayLike, prob: ArrayLike, lower_tail: Bool = True, log_prob: Bool = False, dtype = <class 'jax.numpy.int64'>) -> ArrayLike

Computes the quantile of a binomial distribution.

Parameters:

Name	Type	Description	Default
p	ArrayLike	The probability of success.	required
size	ArrayLike	The number of trials.	required
prob	ArrayLike	The probability of success in each trial.	required
lower_tail	Bool	Whether to compute the lower tail or not. Defaults to True.	True
log_prob	Bool	Whether to compute the log probability or not. Defaults to False.	False
dtype	jnp.int_	The data type of the output array. Defaults to jnp.int_.	<class 'jax.numpy.int64'>

Returns:

Type	Description
ArrayLike	The quantile of the binomial distribution.

Examples:

>>> p = jnp.array([0.1, 0.5, 0.9])
>>> size = 10
>>> prob = 0.5
>>> qbinom(p, size, prob)

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stamox.distribution.dbinom(q: ArrayLike, size: ArrayLike, prob: ArrayLike, lower_tail: Bool = True, log_prob: Bool = False, dtype = <class 'jax.numpy.float64'>) -> ArrayLike

Computes the probability of a binomial distribution.

Parameters:

Name	Type	Description	Default
q	ArrayLike	The value to compute the probability for.	required
size	ArrayLike	The number of trials in the binomial distribution.	required
prob	ArrayLike	The probability of success in each trial.	required
lower_tail	Bool	Whether to compute the lower tail probability. Defaults to True.	True
log_prob	Bool	Whether to return the logarithm of the probability. Defaults to False.	False
dtype	jnp.float_	The data type of the output array. Defaults to jnp.float_.	<class 'jax.numpy.float64'>

Returns:

Type	Description
ArrayLike	The probability of the binomial distribution.

Examples:

>>> q = jnp.array([0.1, 0.5, 0.9])
>>> size = 10
>>> prob = 0.5
>>> dbinom(q, size, prob)

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stamox.distribution.rbinom(key: Union[jax.Array, jax._src.prng.PRNGKeyArray], sample_shape: Optional[Sequence[int]] = None, size: ArrayLike = None, prob: ArrayLike = None, lower_tail: Bool = True, log_prob: Bool = False, dtype = <class 'jax.numpy.int64'>) -> ArrayLike

Generates random binomial samples from a given probability distribution.

Parameters:

Name	Type	Description	Default
key	KeyArray	A random number generator key.	required
sample_shape	Optional[Shape]	The shape of the output array. Defaults to None.	None
size	ArrayLike	The number of trials. Defaults to None.	None
prob	ArrayLike	The probability of success for each trial. Defaults to None.	None
lower_tail	Bool	Whether to return the lower tail of the distribution. Defaults to True.	True
log_prob	Bool	Whether to return the logarithm of the probability. Defaults to False.	False
dtype	jnp.float32	The data type of the output array. Defaults to jnp.float32.	<class 'jax.numpy.int64'>

Returns:

Type	Description
ArrayLike	An array containing the random binomial samples.

Examples:

>>> key = jax.random.PRNGKey(0)
>>> sample_shape = (3, 3)
>>> size = 10
>>> prob = 0.5
>>> rbinom(key, sample_shape, size, prob)