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Distributions

Prior distributions used in the unknown_parameters_prior dict. Each exposes evaluate(x) (the pdf), log_pdf(x), cdf(x) and sample(min, max, seed).

Normal

Bases: object

Normal distribution helper.

The class provides density evaluation and bounded random sampling for a Gaussian distribution parameterized by its mean and standard deviation.

...

Attributes:

Name Type Description
mu float

Mean of the normal distribution.
sigma float

Standard deviation of the normal distribution.

Methods:

Name Description
evaluate

Evaluates the probability density function at x.
sample

Draws a bounded random sample from the distribution.
Source code in src/py_replay_bg/distributions/__init__.py 
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@jitclass_([
    ("mu", float64),
    ("sigma", float64),
])
class Normal(object):
    """Normal distribution helper.

    The class provides density evaluation and bounded random sampling for a
    Gaussian distribution parameterized by its mean and standard deviation.

    ...
    Attributes
    ----------
    mu : float
        Mean of the normal distribution.
    sigma : float
        Standard deviation of the normal distribution.

    Methods
    -------
    evaluate(x):
        Evaluates the probability density function at ``x``.
    sample(min_val, max_val, seed):
        Draws a bounded random sample from the distribution.
    """

    def __init__(self, mu, sigma):
        """Constructs all the necessary attributes for the Normal object.

        Parameters
        ----------
        mu : float
            Mean of the normal distribution.
        sigma : float
            Standard deviation of the normal distribution.
        """
        self.mu = mu
        self.sigma = sigma

    def evaluate(self, x):
        """Evaluates the normal probability density function.

        Parameters
        ----------
        x : float
            Value at which to evaluate the density.

        Returns
        -------
        float
            The probability density value at ``x``.
        """
        return 1 / (self.sigma * np.sqrt(2 * np.pi)) * np.exp(- 0.5 * ((x - self.mu) / self.sigma) ** 2)

    def log_pdf(self, x):
        """Evaluates the log of the normal probability density function.

        Parameters
        ----------
        x : float
            Value at which to evaluate the density.

        Returns
        -------
        float
            The log-density value at ``x``.
        """
        return np.log(self.evaluate(x))

    def cdf(self, x):
        """Evaluates the normal cumulative distribution function.

        Parameters
        ----------
        x : float
            Value at which to evaluate the CDF.

        Returns
        -------
        float
            The cumulative probability at ``x``.
        """
        return 0.5 * (1.0 + math.erf((x - self.mu) / (self.sigma * _SQRT2)))

    def sample(self, min_val, max_val, seed=None):
        """Draws a bounded random sample from the distribution.

        Parameters
        ----------
        min_val : float
            Minimum allowed sampled value.
        max_val : float
            Maximum allowed sampled value.
        seed : int, optional, default : None
            Optional random seed. For reproducibility.

        Returns
        -------
        float
            A sample from the distribution clipped to the given bounds.
        """
        if seed is not None:
            np.random.seed(seed)
        return min(max(np.random.normal(self.mu, self.sigma), min_val), max_val)

mu = mu instance-attribute

sigma = sigma instance-attribute

__init__(mu, sigma)

Constructs all the necessary attributes for the Normal object.

Parameters:

Name Type Description Default
mu float

Mean of the normal distribution.

 required
sigma float

Standard deviation of the normal distribution.

 required
Source code in src/py_replay_bg/distributions/__init__.py 
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def __init__(self, mu, sigma):
    """Constructs all the necessary attributes for the Normal object.

    Parameters
    ----------
    mu : float
        Mean of the normal distribution.
    sigma : float
        Standard deviation of the normal distribution.
    """
    self.mu = mu
    self.sigma = sigma

evaluate(x)

Evaluates the normal probability density function.

Parameters:

Name Type Description Default
x float

Value at which to evaluate the density.

 required

Returns:

Type Description
float

The probability density value at x.
Source code in src/py_replay_bg/distributions/__init__.py 
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def evaluate(self, x):
    """Evaluates the normal probability density function.

    Parameters
    ----------
    x : float
        Value at which to evaluate the density.

    Returns
    -------
    float
        The probability density value at ``x``.
    """
    return 1 / (self.sigma * np.sqrt(2 * np.pi)) * np.exp(- 0.5 * ((x - self.mu) / self.sigma) ** 2)

log_pdf(x)

Evaluates the log of the normal probability density function.

Parameters:

Name Type Description Default
x float

Value at which to evaluate the density.

 required

Returns:

Type Description
float

The log-density value at x.
Source code in src/py_replay_bg/distributions/__init__.py 
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def log_pdf(self, x):
    """Evaluates the log of the normal probability density function.

    Parameters
    ----------
    x : float
        Value at which to evaluate the density.

    Returns
    -------
    float
        The log-density value at ``x``.
    """
    return np.log(self.evaluate(x))

cdf(x)

Evaluates the normal cumulative distribution function.

Parameters:

Name Type Description Default
x float

Value at which to evaluate the CDF.

 required

Returns:

Type Description
float

The cumulative probability at x.
Source code in src/py_replay_bg/distributions/__init__.py 
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def cdf(self, x):
    """Evaluates the normal cumulative distribution function.

    Parameters
    ----------
    x : float
        Value at which to evaluate the CDF.

    Returns
    -------
    float
        The cumulative probability at ``x``.
    """
    return 0.5 * (1.0 + math.erf((x - self.mu) / (self.sigma * _SQRT2)))

sample(min_val, max_val, seed=None)

Draws a bounded random sample from the distribution.

Parameters:

Name Type Description Default
min_val float

Minimum allowed sampled value.

 required
max_val float

Maximum allowed sampled value.

 required
seed int

Optional random seed. For reproducibility.

 : None

Returns:

Type Description
float

A sample from the distribution clipped to the given bounds.
Source code in src/py_replay_bg/distributions/__init__.py 
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def sample(self, min_val, max_val, seed=None):
    """Draws a bounded random sample from the distribution.

    Parameters
    ----------
    min_val : float
        Minimum allowed sampled value.
    max_val : float
        Maximum allowed sampled value.
    seed : int, optional, default : None
        Optional random seed. For reproducibility.

    Returns
    -------
    float
        A sample from the distribution clipped to the given bounds.
    """
    if seed is not None:
        np.random.seed(seed)
    return min(max(np.random.normal(self.mu, self.sigma), min_val), max_val)

LogNormal

Bases: object

Log-normal distribution helper.

The class provides density evaluation and bounded random sampling for a log-normal distribution parameterized by the mean and standard deviation of the underlying normal distribution.

...

Attributes:

Name Type Description
mu float

Mean of the underlying normal distribution.
sigma float

Standard deviation of the underlying normal distribution.

Methods:

Name Description
evaluate

Evaluates the probability density function at x.
sample

Draws a bounded random sample from the distribution.
Source code in src/py_replay_bg/distributions/__init__.py 
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@jitclass_([
    ("mu", float64),
    ("sigma", float64),
])
class LogNormal(object):
    """Log-normal distribution helper.

    The class provides density evaluation and bounded random sampling for a
    log-normal distribution parameterized by the mean and standard deviation
    of the underlying normal distribution.

    ...
    Attributes
    ----------
    mu : float
        Mean of the underlying normal distribution.
    sigma : float
        Standard deviation of the underlying normal distribution.

    Methods
    -------
    evaluate(x):
        Evaluates the probability density function at ``x``.
    sample(min_val, max_val, seed):
        Draws a bounded random sample from the distribution.
    """

    def __init__(self, mu, sigma):
        """Constructs all the necessary attributes for the LogNormal object.

        Parameters
        ----------
        mu : float
            Mean of the underlying normal distribution.
        sigma : float
            Standard deviation of the underlying normal distribution.
        """
        self.mu = mu
        self.sigma = sigma

    def evaluate(self, x):
        """Evaluates the log-normal probability density function.

        Parameters
        ----------
        x : float
            Value at which to evaluate the density. Must be positive.

        Returns
        -------
        float
            The probability density value at ``x``.
        """
        return 1 / (x * self.sigma * np.sqrt(2 * np.pi)) * np.exp(- ((np.log(x) - self.mu) ** 2) / (2 * (self.sigma ** 2)))

    def log_pdf(self, x):
        """Evaluates the log of the log-normal probability density function.

        Parameters
        ----------
        x : float
            Value at which to evaluate the density. Must be positive.

        Returns
        -------
        float
            The log-density value at ``x``.
        """
        return np.log(self.evaluate(x))

    def cdf(self, x):
        """Evaluates the log-normal cumulative distribution function.

        Parameters
        ----------
        x : float
            Value at which to evaluate the CDF.

        Returns
        -------
        float
            The cumulative probability at ``x``. Returns ``0.0`` if ``x <= 0``.
        """
        if x <= 0:
            return 0.0
        return 0.5 * (1.0 + math.erf((np.log(x) - self.mu) / (self.sigma * _SQRT2)))

    def sample(self, min_val, max_val, seed=None):
        """Draws a bounded random sample from the distribution.

        Parameters
        ----------
        min_val : float
            Minimum allowed sampled value.
        max_val : float
            Maximum allowed sampled value.
        seed : int, optional, default : None
            Optional random seed. For reproducibility.

        Returns
        -------
        float
            A sample from the distribution clipped to the given bounds.
        """
        if seed is not None:
            np.random.seed(seed)
        return min(max(np.random.lognormal(self.mu, self.sigma), min_val), max_val)

mu = mu instance-attribute

sigma = sigma instance-attribute

__init__(mu, sigma)

Constructs all the necessary attributes for the LogNormal object.

Parameters:

Name Type Description Default
mu float

Mean of the underlying normal distribution.

 required
sigma float

Standard deviation of the underlying normal distribution.

 required
Source code in src/py_replay_bg/distributions/__init__.py 
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def __init__(self, mu, sigma):
    """Constructs all the necessary attributes for the LogNormal object.

    Parameters
    ----------
    mu : float
        Mean of the underlying normal distribution.
    sigma : float
        Standard deviation of the underlying normal distribution.
    """
    self.mu = mu
    self.sigma = sigma

evaluate(x)

Evaluates the log-normal probability density function.

Parameters:

Name Type Description Default
x float

Value at which to evaluate the density. Must be positive.

 required

Returns:

Type Description
float

The probability density value at x.
Source code in src/py_replay_bg/distributions/__init__.py 
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def evaluate(self, x):
    """Evaluates the log-normal probability density function.

    Parameters
    ----------
    x : float
        Value at which to evaluate the density. Must be positive.

    Returns
    -------
    float
        The probability density value at ``x``.
    """
    return 1 / (x * self.sigma * np.sqrt(2 * np.pi)) * np.exp(- ((np.log(x) - self.mu) ** 2) / (2 * (self.sigma ** 2)))

log_pdf(x)

Evaluates the log of the log-normal probability density function.

Parameters:

Name Type Description Default
x float

Value at which to evaluate the density. Must be positive.

 required

Returns:

Type Description
float

The log-density value at x.
Source code in src/py_replay_bg/distributions/__init__.py 
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def log_pdf(self, x):
    """Evaluates the log of the log-normal probability density function.

    Parameters
    ----------
    x : float
        Value at which to evaluate the density. Must be positive.

    Returns
    -------
    float
        The log-density value at ``x``.
    """
    return np.log(self.evaluate(x))

cdf(x)

Evaluates the log-normal cumulative distribution function.

Parameters:

Name Type Description Default
x float

Value at which to evaluate the CDF.

 required

Returns:

Type Description
float

The cumulative probability at x. Returns 0.0 if x <= 0.
Source code in src/py_replay_bg/distributions/__init__.py 
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def cdf(self, x):
    """Evaluates the log-normal cumulative distribution function.

    Parameters
    ----------
    x : float
        Value at which to evaluate the CDF.

    Returns
    -------
    float
        The cumulative probability at ``x``. Returns ``0.0`` if ``x <= 0``.
    """
    if x <= 0:
        return 0.0
    return 0.5 * (1.0 + math.erf((np.log(x) - self.mu) / (self.sigma * _SQRT2)))

sample(min_val, max_val, seed=None)

Draws a bounded random sample from the distribution.

Parameters:

Name Type Description Default
min_val float

Minimum allowed sampled value.

 required
max_val float

Maximum allowed sampled value.

 required
seed int

Optional random seed. For reproducibility.

 : None

Returns:

Type Description
float

A sample from the distribution clipped to the given bounds.
Source code in src/py_replay_bg/distributions/__init__.py 
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def sample(self, min_val, max_val, seed=None):
    """Draws a bounded random sample from the distribution.

    Parameters
    ----------
    min_val : float
        Minimum allowed sampled value.
    max_val : float
        Maximum allowed sampled value.
    seed : int, optional, default : None
        Optional random seed. For reproducibility.

    Returns
    -------
    float
        A sample from the distribution clipped to the given bounds.
    """
    if seed is not None:
        np.random.seed(seed)
    return min(max(np.random.lognormal(self.mu, self.sigma), min_val), max_val)

Gamma

Gamma distribution helper.

The class provides density evaluation and bounded random sampling for a Gamma distribution parameterized in rate form.

...

Attributes:

Name Type Description
alpha float

Shape parameter.
beta float

Rate parameter, where beta = 1 / scale.
_log_normalizer float

Cached log-normalization constant.

Methods:

Name Description
evaluate

Evaluates the probability density function at x.
sample

Draws a bounded random sample from the distribution.
Source code in src/py_replay_bg/distributions/__init__.py 
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@jitclass_([
    ("alpha", float64),
    ("beta", float64),
    ("_log_normalizer", float64),
])
class Gamma:
    """Gamma distribution helper.

    The class provides density evaluation and bounded random sampling for a
    Gamma distribution parameterized in rate form.

    ...
    Attributes
    ----------
    alpha : float
        Shape parameter.
    beta : float
        Rate parameter, where ``beta = 1 / scale``.
    _log_normalizer : float
        Cached log-normalization constant.

    Methods
    -------
    evaluate(x):
        Evaluates the probability density function at ``x``.
    sample(min_val, max_val, seed):
        Draws a bounded random sample from the distribution.
    """

    def __init__(self, alpha, beta):
        """Constructs all the necessary attributes for the Gamma object.

        Parameters
        ----------
        alpha : float
            Shape parameter.
        beta : float
            Rate parameter, where ``beta = 1 / scale``.
        """
        self.alpha = alpha
        self.beta = beta  # rate parameterization (beta = 1/scale)
        self._log_normalizer = alpha * np.log(beta) - _gammaln(alpha)

    def evaluate(self, x):
        """Evaluates the Gamma probability density function.

        Parameters
        ----------
        x : float
            Value at which to evaluate the density. Must be positive.

        Returns
        -------
        float
            The probability density value at ``x``. Returns ``0.0`` if
            ``x <= 0``.
        """
        if x <= 0:
            return 0.0
        return np.exp(self._log_normalizer + (self.alpha - 1) * np.log(x) - self.beta * x)

    def log_pdf(self, x):
        """Evaluates the log of the Gamma probability density function.

        Computed directly in log space (not as ``log(evaluate(x))``), since
        routing through ``exp`` and back loses precision relative to the
        closed-form log-density.

        Parameters
        ----------
        x : float
            Value at which to evaluate the density. Must be positive.

        Returns
        -------
        float
            The log-density value at ``x``. Returns ``-inf`` if ``x <= 0``.
        """
        if x <= 0:
            return -np.inf
        return self.alpha * np.log(self.beta) + (self.alpha - 1.0) * np.log(x) - self.beta * x - _gammaln(self.alpha)

    def cdf(self, x):
        """Evaluates the Gamma cumulative distribution function.

        Uses the regularized lower incomplete gamma function ``P(alpha, beta*x)``.

        Parameters
        ----------
        x : float
            Value at which to evaluate the CDF.

        Returns
        -------
        float
            The cumulative probability at ``x``. Returns ``0.0`` if ``x <= 0``.
        """
        if x <= 0:
            return 0.0
        return _gammainc_lower_reg(self.alpha, self.beta * x)

    def sample(self, min_val, max_val, seed=None):
        """Draws a bounded random sample from the distribution.

        Parameters
        ----------
        min_val : float
            Minimum allowed sampled value.
        max_val : float
            Maximum allowed sampled value.
        seed : int, optional, default : None
            Optional random seed. For reproducibility.

        Returns
        -------
        float
            A sample from the distribution clipped to the given bounds.
        """
        if seed is not None:
            np.random.seed(seed)
        return min(max(np.random.gamma(self.alpha, 1.0 / self.beta), min_val), max_val)

alpha = alpha instance-attribute

beta = beta instance-attribute

_log_normalizer = alpha * np.log(beta) - _gammaln(alpha) instance-attribute

__init__(alpha, beta)

Constructs all the necessary attributes for the Gamma object.

Parameters:

Name Type Description Default
alpha float

Shape parameter.

 required
beta float

Rate parameter, where beta = 1 / scale.

 required
Source code in src/py_replay_bg/distributions/__init__.py 
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def __init__(self, alpha, beta):
    """Constructs all the necessary attributes for the Gamma object.

    Parameters
    ----------
    alpha : float
        Shape parameter.
    beta : float
        Rate parameter, where ``beta = 1 / scale``.
    """
    self.alpha = alpha
    self.beta = beta  # rate parameterization (beta = 1/scale)
    self._log_normalizer = alpha * np.log(beta) - _gammaln(alpha)

evaluate(x)

Evaluates the Gamma probability density function.

Parameters:

Name Type Description Default
x float

Value at which to evaluate the density. Must be positive.

 required

Returns:

Type Description
float

The probability density value at x. Returns 0.0 if x <= 0.
Source code in src/py_replay_bg/distributions/__init__.py 
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def evaluate(self, x):
    """Evaluates the Gamma probability density function.

    Parameters
    ----------
    x : float
        Value at which to evaluate the density. Must be positive.

    Returns
    -------
    float
        The probability density value at ``x``. Returns ``0.0`` if
        ``x <= 0``.
    """
    if x <= 0:
        return 0.0
    return np.exp(self._log_normalizer + (self.alpha - 1) * np.log(x) - self.beta * x)

log_pdf(x)

Evaluates the log of the Gamma probability density function.

Computed directly in log space (not as log(evaluate(x))), since routing through exp and back loses precision relative to the closed-form log-density.

Parameters:

Name Type Description Default
x float

Value at which to evaluate the density. Must be positive.

 required

Returns:

Type Description
float

The log-density value at x. Returns -inf if x <= 0.
Source code in src/py_replay_bg/distributions/__init__.py 
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def log_pdf(self, x):
    """Evaluates the log of the Gamma probability density function.

    Computed directly in log space (not as ``log(evaluate(x))``), since
    routing through ``exp`` and back loses precision relative to the
    closed-form log-density.

    Parameters
    ----------
    x : float
        Value at which to evaluate the density. Must be positive.

    Returns
    -------
    float
        The log-density value at ``x``. Returns ``-inf`` if ``x <= 0``.
    """
    if x <= 0:
        return -np.inf
    return self.alpha * np.log(self.beta) + (self.alpha - 1.0) * np.log(x) - self.beta * x - _gammaln(self.alpha)

cdf(x)

Evaluates the Gamma cumulative distribution function.

Uses the regularized lower incomplete gamma function P(alpha, beta*x).

Parameters:

Name Type Description Default
x float

Value at which to evaluate the CDF.

 required

Returns:

Type Description
float

The cumulative probability at x. Returns 0.0 if x <= 0.
Source code in src/py_replay_bg/distributions/__init__.py 
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def cdf(self, x):
    """Evaluates the Gamma cumulative distribution function.

    Uses the regularized lower incomplete gamma function ``P(alpha, beta*x)``.

    Parameters
    ----------
    x : float
        Value at which to evaluate the CDF.

    Returns
    -------
    float
        The cumulative probability at ``x``. Returns ``0.0`` if ``x <= 0``.
    """
    if x <= 0:
        return 0.0
    return _gammainc_lower_reg(self.alpha, self.beta * x)

sample(min_val, max_val, seed=None)

Draws a bounded random sample from the distribution.

Parameters:

Name Type Description Default
min_val float

Minimum allowed sampled value.

 required
max_val float

Maximum allowed sampled value.

 required
seed int

Optional random seed. For reproducibility.

 : None

Returns:

Type Description
float

A sample from the distribution clipped to the given bounds.
Source code in src/py_replay_bg/distributions/__init__.py 
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def sample(self, min_val, max_val, seed=None):
    """Draws a bounded random sample from the distribution.

    Parameters
    ----------
    min_val : float
        Minimum allowed sampled value.
    max_val : float
        Maximum allowed sampled value.
    seed : int, optional, default : None
        Optional random seed. For reproducibility.

    Returns
    -------
    float
        A sample from the distribution clipped to the given bounds.
    """
    if seed is not None:
        np.random.seed(seed)
    return min(max(np.random.gamma(self.alpha, 1.0 / self.beta), min_val), max_val)

Uniform

Bases: object

Uniform distribution helper.

The class provides density evaluation and bounded random sampling for a uniform distribution over the interval [a, b].

...

Attributes:

Name Type Description
a float

Lower bound of the distribution support.
b float

Upper bound of the distribution support.

Methods:

Name Description
evaluate

Evaluates the probability density function at x.
sample

Draws a bounded random sample from the distribution.
Source code in src/py_replay_bg/distributions/__init__.py 
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@jitclass_([
    ("a", float64),
    ("b", float64),
])
class Uniform(object):
    """Uniform distribution helper.

    The class provides density evaluation and bounded random sampling for a
    uniform distribution over the interval ``[a, b]``.

    ...
    Attributes
    ----------
    a : float
        Lower bound of the distribution support.
    b : float
        Upper bound of the distribution support.

    Methods
    -------
    evaluate(x):
        Evaluates the probability density function at ``x``.
    sample(min_val, max_val, seed):
        Draws a bounded random sample from the distribution.
    """

    def __init__(self, a, b):
        """Constructs all the necessary attributes for the Uniform object.

        Parameters
        ----------
        a : float
            Lower bound of the distribution support.
        b : float
            Upper bound of the distribution support.
        """
        self.a = a
        self.b = b

    def evaluate(self, x):
        """Evaluates the uniform probability density function.

        Parameters
        ----------
        x : float
            Value at which to evaluate the density.

        Returns
        -------
        float
            The probability density value at ``x``. Returns ``0.0`` if ``x`` is
            outside ``[a, b]``.
        """
        if x < self.a or x > self.b:
            return 0.0
        return 1.0 / (self.b - self.a)

    def log_pdf(self, x):
        """Evaluates the log of the uniform probability density function.

        Parameters
        ----------
        x : float
            Value at which to evaluate the density.

        Returns
        -------
        float
            The log-density value at ``x``. Returns ``-inf`` if ``x`` is
            outside ``[a, b]``.
        """
        if x < self.a or x > self.b:
            return -np.inf
        return -np.log(self.b - self.a)

    def cdf(self, x):
        """Evaluates the uniform cumulative distribution function.

        Parameters
        ----------
        x : float
            Value at which to evaluate the CDF.

        Returns
        -------
        float
            The cumulative probability at ``x``, clipped to ``[0, 1]``.
        """
        if x <= self.a:
            return 0.0
        if x >= self.b:
            return 1.0
        return (x - self.a) / (self.b - self.a)

    def sample(self, min_val, max_val, seed=None):
        """Draws a bounded random sample from the distribution.

        Parameters
        ----------
        min_val : float
            Minimum allowed sampled value.
        max_val : float
            Maximum allowed sampled value.
        seed : int, optional, default : None
            Optional random seed. For reproducibility.

        Returns
        -------
        float
            A sample from the distribution clipped to the given bounds.
        """
        if seed is not None:
            np.random.seed(seed)
        return min(max(np.random.uniform(self.a, self.b), min_val), max_val)

a = a instance-attribute

b = b instance-attribute

__init__(a, b)

Constructs all the necessary attributes for the Uniform object.

Parameters:

Name Type Description Default
a float

Lower bound of the distribution support.

 required
b float

Upper bound of the distribution support.

 required
Source code in src/py_replay_bg/distributions/__init__.py 
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def __init__(self, a, b):
    """Constructs all the necessary attributes for the Uniform object.

    Parameters
    ----------
    a : float
        Lower bound of the distribution support.
    b : float
        Upper bound of the distribution support.
    """
    self.a = a
    self.b = b

evaluate(x)

Evaluates the uniform probability density function.

Parameters:

Name Type Description Default
x float

Value at which to evaluate the density.

 required

Returns:

Type Description
float

The probability density value at x. Returns 0.0 if x is outside [a, b].
Source code in src/py_replay_bg/distributions/__init__.py 
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def evaluate(self, x):
    """Evaluates the uniform probability density function.

    Parameters
    ----------
    x : float
        Value at which to evaluate the density.

    Returns
    -------
    float
        The probability density value at ``x``. Returns ``0.0`` if ``x`` is
        outside ``[a, b]``.
    """
    if x < self.a or x > self.b:
        return 0.0
    return 1.0 / (self.b - self.a)

log_pdf(x)

Evaluates the log of the uniform probability density function.

Parameters:

Name Type Description Default
x float

Value at which to evaluate the density.

 required

Returns:

Type Description
float

The log-density value at x. Returns -inf if x is outside [a, b].
Source code in src/py_replay_bg/distributions/__init__.py 
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def log_pdf(self, x):
    """Evaluates the log of the uniform probability density function.

    Parameters
    ----------
    x : float
        Value at which to evaluate the density.

    Returns
    -------
    float
        The log-density value at ``x``. Returns ``-inf`` if ``x`` is
        outside ``[a, b]``.
    """
    if x < self.a or x > self.b:
        return -np.inf
    return -np.log(self.b - self.a)

cdf(x)

Evaluates the uniform cumulative distribution function.

Parameters:

Name Type Description Default
x float

Value at which to evaluate the CDF.

 required

Returns:

Type Description
float

The cumulative probability at x, clipped to [0, 1].
Source code in src/py_replay_bg/distributions/__init__.py 
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def cdf(self, x):
    """Evaluates the uniform cumulative distribution function.

    Parameters
    ----------
    x : float
        Value at which to evaluate the CDF.

    Returns
    -------
    float
        The cumulative probability at ``x``, clipped to ``[0, 1]``.
    """
    if x <= self.a:
        return 0.0
    if x >= self.b:
        return 1.0
    return (x - self.a) / (self.b - self.a)

sample(min_val, max_val, seed=None)

Draws a bounded random sample from the distribution.

Parameters:

Name Type Description Default
min_val float

Minimum allowed sampled value.

 required
max_val float

Maximum allowed sampled value.

 required
seed int

Optional random seed. For reproducibility.

 : None

Returns:

Type Description
float

A sample from the distribution clipped to the given bounds.
Source code in src/py_replay_bg/distributions/__init__.py 
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def sample(self, min_val, max_val, seed=None):
    """Draws a bounded random sample from the distribution.

    Parameters
    ----------
    min_val : float
        Minimum allowed sampled value.
    max_val : float
        Maximum allowed sampled value.
    seed : int, optional, default : None
        Optional random seed. For reproducibility.

    Returns
    -------
    float
        A sample from the distribution clipped to the given bounds.
    """
    if seed is not None:
        np.random.seed(seed)
    return min(max(np.random.uniform(self.a, self.b), min_val), max_val)